Download or read book Mutations of Alternative Algebras written by Alberto Elduque and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Around 1978, a mutation of associative algebras was introduced to generalize the formalism of classical mechanics as well as quantum mechanics. This volume presents the first book devoted to a self-contained and detailed treatment of the mathematical theory of mutation algebras, which is based on research in this subject over the past fifteen years. The book also deals with a broader class of algebras, mutations of alternative algebras, which are a natural generalization of mutations of associative algebras. A complete structure theory, including automorphisms, derivations and certain representations, is given for mutations of artinian alternative algebras, and, in particular, of Cayley--Dickson algebras. Since the mutation algebras do not form a variety, the structure theory explored in this volume takes quite a different approach from the standard theory of nonassociative algebras and provides an important interplay with the theory of noncommutative (associative) algebras through mutation parameters. New simple algebras and open problems presented in this book will stimulate additional research and applications in the area. This book will be valuable to graduate students, mathematicians and physicists interested in applications of algebras.

Download or read book Second International Conference on Algebra written by Leonid Arkadʹevich Bokutʹ and published by American Mathematical Soc.. This book was released on 1995 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains papers presented at the Second International Conference on Algebra, held in Barnaul in August 1991 in honour of the memory of A. I. Shirshov (1921--1981). Many of the results presented here have not been published elsewhere in the literature. The collection provides a panorama of current research in PI-, associative, Lie, and Jordan algebras and discusses the interrelations of these areas with geometry and physics. Other topics in group theory and homological algebra are also covered.

Download or read book Algebra without Borders Classical and Constructive Nonassociative Algebraic Structures written by Mahouton Norbert Hounkonnou and published by Springer Nature. This book was released on 2023-12-01 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers invited, peer-reviewed works presented at the 2021 edition of the Classical and Constructive Nonassociative Algebraic Structures: Foundations and Applications—CaCNAS: FA 2021, virtually held from June 30 to July 2, 2021, in dedication to the memory of Professor Nebojša Stevanović (1962-2009). The papers cover new trends in the field, focusing on the growing development of applications in other disciplines. These aspects interplay in the same cadence, promoting interactions between theory and applications, and between nonassociative algebraic structures and various fields in pure and applied mathematics. In this volume, the reader will find novel studies on topics such as left almost algebras, logical algebras, groupoids and their generalizations, algebraic geometry and its relations with quiver algebras, enumerative combinatorics, representation theory, fuzzy logic and foundation theory, fuzzy algebraic structures, group amalgams, computer-aided development and transformation of the theory of nonassociative algebraic structures, and applications within natural sciences and engineering. Researchers and graduate students in algebraic structures and their applications can hugely benefit from this book, which can also interest any researcher exploring multi-disciplinarity and complexity in the scientific realm.

Download or read book Algebra and Applications 1 written by Abdenacer Makhlouf and published by John Wiley & Sons. This book was released on 2021-03-31 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is part of Algebra and Geometry, a subject within the SCIENCES collection published by ISTE and Wiley, and the first of three volumes specifically focusing on algebra and its applications. Algebra and Applications 1 centers on non-associative algebras and includes an introduction to derived categories. The chapters are written by recognized experts in the field, providing insight into new trends, as well as a comprehensive introduction to the theory. The book incorporates self-contained surveys with the main results, applications and perspectives. The chapters in this volume cover a wide variety of algebraic structures and their related topics. Jordan superalgebras, Lie algebras, composition algebras, graded division algebras, non-associative C*- algebras, H*-algebras, Krichever-Novikov type algebras, preLie algebras and related structures, geometric structures on 3-Lie algebras and derived categories are all explored. Algebra and Applications 1 is of great interest to graduate students and researchers. Each chapter combines some of the features of both a graduate level textbook and of research level surveys.

Download or read book Non Associative Normed Algebras written by Miguel Cabrera García and published by Cambridge University Press. This book was released on 2018-04-12 with total page 759 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first systematic account of the basic theory of normed algebras, without assuming associativity. Sure to become a central resource.

Download or read book Non Associative Normed Algebras Volume 2 Representation Theory and the Zel manov Approach written by Miguel Cabrera García and published by Cambridge University Press. This book was released on 2018-04-12 with total page 759 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field. This second volume revisits JB*-triples, covers Zel'manov's celebrated work in Jordan theory, proves the unit-free variant of the Vidav–Palmer theorem, and develops the representation theory of alternative C*-algebras and non-commutative JB*-algebras. This completes the work begun in the first volume, which introduced these algebras and discussed the so-called non-associative Gelfand–Naimark and Vidav–Palmer theorems. This book interweaves pure algebra, geometry of normed spaces, and infinite-dimensional complex analysis. Novel proofs are presented in complete detail at a level accessible to graduate students. The book contains a wealth of historical comments, background material, examples, and an extensive bibliography.

Download or read book Smarandache Non Associative Rings written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on 2002 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generally, in any human field, a Smarandache Structure on a set A means a weak structure W on A such that there exists a proper subset B in A which is embedded with a stronger structure S. These types of structures occur in our everyday's life, that's why we study them in this book. Thus, as a particular case: A Non-associative ring is a non-empty set R together with two binary operations '+' and '.' such that (R, +) is an additive abelian group and (R, .) is a groupoid. For all a, b, c in R we have (a + b) . c = a . c + b . c and c . (a + b) = c . a + c . b. A Smarandache non-associative ring is a non-associative ring (R, +, .) which has a proper subset P in R, that is an associative ring (with respect to the same binary operations on R).

Download or read book Subset Non Associative Semirings written by W. B. Vasantha Kandasamy and published by Infinite Study. This book was released on with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Lie Groups and Lie Algebras written by B.P. Komrakov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 442 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection contains papers conceptually related to the classical ideas of Sophus Lie (i.e., to Lie groups and Lie algebras). Obviously, it is impos sible to embrace all such topics in a book of reasonable size. The contents of this one reflect the scientific interests of those authors whose activities, to some extent at least, are associated with the International Sophus Lie Center. We have divided the book into five parts in accordance with the basic topics of the papers (although it can be easily seen that some of them may be attributed to several parts simultaneously). The first part (quantum mathematics) combines the papers related to the methods generated by the concepts of quantization and quantum group. The second part is devoted to the theory of hypergroups and Lie hypergroups, which is one of the most important generalizations of the classical concept of locally compact group and of Lie group. A natural harmonic analysis arises on hypergroups, while any abstract transformation of Fourier type is gen erated by some hypergroup (commutative or not). Part III contains papers on the geometry of homogeneous spaces, Lie algebras and Lie superalgebras. Classical problems of the representation theory for Lie groups, as well as for topological groups and semigroups, are discussed in the papers of Part IV. Finally, the last part of the collection relates to applications of the ideas of Sophus Lie to differential equations.

Download or read book Non Associative Algebras and Related Topics written by Helena Albuquerque and published by Springer Nature. This book was released on 2023-07-28 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume presents a selection of peer-reviewed contributions from the Second Non-Associative Algebras and Related Topics (NAART II) conference, which was held at the University of Coimbra, Portugal, from July 18–22, 2022. The conference was held in honor of mathematician Alberto Elduque, who has made significant contributions to the study of non-associative structures such as Lie, Jordan, and Leibniz algebras. The papers in this volume are organized into four parts: Lie algebras, superalgebras, and groups; Leibniz algebras; associative and Jordan algebras; and other non-associative structures. They cover a variety of topics, including classification problems, special maps (automorphisms, derivations, etc.), constructions that relate different structures, and representation theory. One of the unique features of NAART is that it is open to all topics related to non-associative algebras, including octonion algebras, composite algebras, Banach algebras, connections with geometry, applications in coding theory, combinatorial problems, and more. This diversity allows researchers from a range of fields to find the conference subjects interesting and discover connections with their own areas, even if they are not traditionally considered non-associative algebraists. Since its inception in 2011, NAART has been committed to fostering cross-disciplinary connections in the study of non-associative structures.

Download or read book Jordan Real and Lie Structures in Operator Algebras written by Sh. Ayupov and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of operator algebras acting on a Hilbert space was initiated in thirties by papers of Murray and von Neumann. In these papers they have studied the structure of algebras which later were called von Neu mann algebras or W* -algebras. They are weakly closed complex *-algebras of operators on a Hilbert space. At present the theory of von Neumann algebras is a deeply developed theory with various applications. In the framework of von Neumann algebras theory the study of fac tors (i.e. W* -algebras with trivial centres) is very important, since they are comparatively simple and investigation of general W* -algebras can be reduced to the case of factors. Therefore the theory of factors is one of the main tools in the structure theory of von Neumann algebras. In the middle of sixtieth Topping [To 1] and Stormer [S 2] have ini tiated the study of Jordan (non associative and real) analogues of von Neumann algebras - so called JW-algebras, i.e. real linear spaces of self adjoint opera.tors on a complex Hilbert space, which contain the identity operator 1. closed with respect to the Jordan (i.e. symmetrised) product INTRODUCTION 2 x 0 y = ~(Xy + yx) and closed in the weak operator topology. The structure of these algebras has happened to be close to the struc ture of von Neumann algebras and it was possible to apply ideas and meth ods similar to von Neumann algebras theory in the study of JW-algebras.

Download or read book Clifford Algebras and Spinor Structures written by Rafal Ablamowicz and published by Springer Science & Business Media. This book was released on 1995-02-28 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume introduces mathematicians and physicists to a crossing point of algebra, physics, differential geometry and complex analysis. The book follows the French tradition of Cartan, Chevalley and Crumeyrolle and summarizes Crumeyrolle's own work on exterior algebra and spinor structures. The depth and breadth of Crumeyrolle's research interests and influence in the field is investigated in a number of articles. Of interest to physicists is the modern presentation of Crumeyrolle's approach to Weyl spinors, and to his spinoriality groups, which are formulated with spinor operators of Kustaanheimo and Hestenes. The Dirac equation and Dirac operator are studied both from the complex analytic and differential geometric points of view, in the modern sense of Ryan and Trautman. For mathematicians and mathematical physicists whose research involves algebra, quantum mechanics and differential geometry.

Download or read book Non Associative Normed Algebras Volume 1 The Vidav Palmer and Gelfand Naimark Theorems written by Miguel Cabrera García and published by Cambridge University Press. This book was released on 2014-07-31 with total page 735 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field. This first volume focuses on the non-associative generalizations of (associative) C*-algebras provided by the so-called non-associative Gelfand–Naimark and Vidav–Palmer theorems, which give rise to alternative C*-algebras and non-commutative JB*-algebras, respectively. The relationship between non-commutative JB*-algebras and JB*-triples is also fully discussed. The second volume covers Zel'manov's celebrated work in Jordan theory to derive classification theorems for non-commutative JB*-algebras and JB*-triples, as well as other topics. The book interweaves pure algebra, geometry of normed spaces, and complex analysis, and includes a wealth of historical comments, background material, examples and exercises. The authors also provide an extensive bibliography.

Download or read book Algebraic Structures and Operators Calculus written by P. Feinsilver and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction I. General remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 II. Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 III. Lie algebras: some basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Chapter 1 Operator calculus and Appell systems I. Boson calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 II. Holomorphic canonical calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 III. Canonical Appell systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Chapter 2 Representations of Lie groups I. Coordinates on Lie groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 II. Dual representations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 III. Matrix elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 IV. Induced representations and homogeneous spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 General Appell systems Chapter 3 I. Convolution and stochastic processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 II. Stochastic processes on Lie groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 III. Appell systems on Lie groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Chapter 4 Canonical systems in several variables I. Homogeneous spaces and Cartan decompositions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 II. Induced representation and coherent states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 III. Orthogonal polynomials in several variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 Chapter 5 Algebras with discrete spectrum I. Calculus on groups: review of the theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 II. Finite-difference algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 III. q-HW algebra and basic hypergeometric functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 IV. su2 and Krawtchouk polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 V. e2 and Lommel polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 Chapter 6 Nilpotent and solvable algebras I. Heisenberg algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 II. Type-H Lie algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 Vll III. Upper-triangular matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125 IV. Affine and Euclidean algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Chapter 7 Hermitian symmetric spaces I. Basic structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 II. Space of rectangular matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 III. Space of skew-symmetric matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 IV. Space of symmetric matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 Chapter 8 Properties of matrix elements I. Addition formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 II. Recurrences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 III. Quotient representations and summation formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 Chapter 9 Symbolic computations I. Computing the pi-matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 II. Adjoint group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 III. Recursive computation of matrix elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Download or read book Algebraic Integrability of Nonlinear Dynamical Systems on Manifolds written by A.K. Prykarpatsky and published by Springer Science & Business Media. This book was released on 2013-04-09 with total page 555 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent times it has been stated that many dynamical systems of classical mathematical physics and mechanics are endowed with symplectic structures, given in the majority of cases by Poisson brackets. Very often such Poisson structures on corresponding manifolds are canonical, which gives rise to the possibility of producing their hidden group theoretical essence for many completely integrable dynamical systems. It is a well understood fact that great part of comprehensive integrability theories of nonlinear dynamical systems on manifolds is based on Lie-algebraic ideas, by means of which, in particular, the classification of such compatibly bi Hamiltonian and isospectrally Lax type integrable systems has been carried out. Many chapters of this book are devoted to their description, but to our regret so far the work has not been completed. Hereby our main goal in each analysed case consists in separating the basic algebraic essence responsible for the complete integrability, and which is, at the same time, in some sense universal, i. e. , characteristic for all of them. Integrability analysis in the framework of a gradient-holonomic algorithm, devised in this book, is fulfilled through three stages: 1) finding a symplectic structure (Poisson bracket) transforming an original dynamical system into a Hamiltonian form; 2) finding first integrals (action variables or conservation laws); 3) defining an additional set of variables and some functional operator quantities with completely controlled evolutions (for instance, as Lax type representation).

Download or read book The Theory of Partial Algebraic Operations written by E.S. Ljapin and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nowadays algebra is understood basically as the general theory of algebraic oper ations and relations. It is characterised by a considerable intrinsic naturalness of its initial notions and problems, the unity of its methods, and a breadth that far exceeds that of its basic concepts. It is more often that its power begins to be displayed when one moves outside its own limits. This characteristic ability is seen when one investigates not only complete operations, but partial operations. To a considerable extent these are related to algebraic operators and algebraic operations. The tendency to ever greater generality is amongst the reasons that playa role in explaining this development. But other important reasons play an even greater role. Within this same theory of total operations (that is, operations defined everywhere), there persistently arises in its different sections a necessity of examining the emergent feature of various partial operations. It is particularly important that this has been found in those parts of algebra it brings together and other areas of mathematics it interacts with as well as where algebra finds applica tion at the very limits of mathematics. In this connection we mention the theory of the composition of mappings, category theory, the theory of formal languages and the related theory of mathematical linguistics, coding theory, information theory, and algebraic automata theory. In all these areas (as well as in others) from time to time there arises the need to consider one or another partial operation.

Download or read book Mathematical Reviews written by and published by . This book was released on 1996 with total page 638 pages. Available in PDF, EPUB and Kindle. Book excerpt: