Download or read book Lie admissible Structures on Witt Type Algebras and Automorphic Algebras written by Mikaël Chopp and published by . This book was released on 2011 with total page 6 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Witt algebra has been intensively studied and arise in many research fields in Mathematics. We are interested in two generalizations of the Witt algebra: the Witt type algebras and the Krichever-Novikov algebras. In a first part we study the problem of finding Lie-admissible structures on Witt type algebras. We give all third-power associative Lie-admissible structures and flexible Lie-admissible structures on these algebras. Moreover we study the symplectic forms which induce a graded left-symmetric product. In the second part of the thesis we study the automorphic algebras. Starting from arbitrary compact Riemann surfaces we consider the action of finite subgroups of the automorphism group of the surface on certain geometrically defined Lie algebras as the Krichever-Novikov type algebras. More precisely, we relate for G a finite subgroup of automorphism acting on the Riemann surface, the invariance subalgebras living on the surface to the algebras on the quotient surface under the group action. The almost-graded Krichever-Novikov algebras structure on the quotient gives in this way a subalgebra of a certain Krichever-Novikov algebra (with almost-grading) on the original Riemann surface.
Download or read book Krichever Novikov Type Algebras written by Martin Schlichenmaier and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-08-19 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: Krichever and Novikov introduced certain classes of infinite dimensional Lie algebras to extend the Virasoro algebra and its related algebras to Riemann surfaces of higher genus. The author of this book generalized and extended them to a more general setting needed by the applications. Examples of applications are Conformal Field Theory, Wess-Zumino-Novikov-Witten models, moduli space problems, integrable systems, Lax operator algebras, and deformation theory of Lie algebra. Furthermore they constitute an important class of infinite dimensional Lie algebras which due to their geometric origin are still manageable. This book gives an introduction for the newcomer to this exciting field of ongoing research in mathematics and will be a valuable source of reference for the experienced researcher. Beside the basic constructions and results also applications are presented.
Download or read book Algebra and Applications 1 written by Abdenacer Makhlouf and published by John Wiley & Sons. This book was released on 2021-05-11 with total page 370 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 Lie Algebras Lie Superalgebras Vertex Algebras and Related Topics written by Kailash C. Misra and published by American Mathematical Soc.. This book was released on 2016-06-28 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of the 2012–2014 Southeastern Lie Theory Workshop Series held at North Carolina State University in April 2012, at College of Charleston in December 2012, at Louisiana State University in May 2013, and at University of Georgia in May 2014. Some of the articles by experts in the field survey recent developments while others include new results in representations of Lie algebras, and quantum groups, vertex (operator) algebras and Lie superalgebras.
Download or read book Krichever Novikov Type Algebras written by Martin Schlichenmaier and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-08-19 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Krichever and Novikov introduced certain classes of infinite dimensional Lie algebras to extend the Virasoro algebra and its related algebras to Riemann surfaces of higher genus. The author of this book generalized and extended them to a more general setting needed by the applications. Examples of applications are Conformal Field Theory, Wess-Zumino-Novikov-Witten models, moduli space problems, integrable systems, Lax operator algebras, and deformation theory of Lie algebra. Furthermore they constitute an important class of infinite dimensional Lie algebras which due to their geometric origin are still manageable. This book gives an introduction for the newcomer to this exciting field of ongoing research in mathematics and will be a valuable source of reference for the experienced researcher. Beside the basic constructions and results also applications are presented.
Download or read book Classical Lie Algebras at Infinity written by Ivan Penkov and published by Springer Nature. This book was released on 2022-01-05 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originating from graduate topics courses given by the first author, this book functions as a unique text-monograph hybrid that bridges a traditional graduate course to research level representation theory. The exposition includes an introduction to the subject, some highlights of the theory and recent results in the field, and is therefore appropriate for advanced graduate students entering the field as well as research mathematicians wishing to expand their knowledge. The mathematical background required varies from chapter to chapter, but a standard course on Lie algebras and their representations, along with some knowledge of homological algebra, is necessary. Basic algebraic geometry and sheaf cohomology are needed for Chapter 10. Exercises of various levels of difficulty are interlaced throughout the text to add depth to topical comprehension. The unifying theme of this book is the structure and representation theory of infinite-dimensional locally reductive Lie algebras and superalgebras. Chapters 1-6 are foundational; each of the last 4 chapters presents a self-contained study of a specialized topic within the larger field. Lie superalgebras and flag supermanifolds are discussed in Chapters 3, 7, and 10, and may be skipped by the reader.
Download or read book On a Covering Group for an Automorphism Group of a Lie Algebra of Classical Type written by Daniel J. Sterling and published by . This book was released on 1962 with total page 144 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Grobner Shirshov Bases Normal Forms Combinatorial and Decision Problems in Algebra written by Leonid Bokut and published by World Scientific Publishing Company. This book was released on 2018 with total page 450 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is about (associative, Lie and other) algebras, groups, semigroups presented by generators and defining relations. They play a great role in modern mathematics. It is enough to mention the quantum groups and Hopf algebra theory, the Kac–Moody and Borcherds algebra theory, the braid groups and Hecke algebra theory, the Coxeter groups and semisimple Lie algebra theory, the plactic monoid theory. One of the main problems for such presentations is the problem of normal forms of their elements. Classical examples of such normal forms give the Poincaré–Birkhoff–Witt theorem for universal enveloping algebras and Artin–Markov normal form theorem for braid groups in Burau generators.What is now called Gröbner–Shirshov bases theory is a general approach to the problem. It was created by a Russian mathematician A I Shirshov (1921–1981) for Lie algebras (explicitly) and associative algebras (implicitly) in 1962. A few years later, H Hironaka created a theory of standard bases for topological commutative algebra and B Buchberger initiated this kind of theory for commutative algebras, the Gröbner basis theory. The Shirshov paper was largely unknown outside Russia. The book covers this gap in the modern mathematical literature. Now Gröbner–Shirshov bases method has many applications both for classical algebraic structures (associative, Lie algebra, groups, semigroups) and new structures (dialgebra, pre-Lie algebra, Rota–Baxter algebra, operads). This is a general and powerful method in algebra.
Download or read book Mathematical Reviews written by and published by . This book was released on 2005 with total page 1884 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Physics Briefs written by and published by . This book was released on 1980 with total page 1038 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 743 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
Download or read book Langlands Correspondence for Loop Groups written by Edward Frenkel and published by Cambridge University Press. This book was released on 2007-06-28 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first account of local geometric Langlands Correspondence, a new area of mathematical physics developed by the author.
Download or read book Lie Groups written by Daniel Bump and published by Springer Science & Business Media. This book was released on 2013-10-01 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended for a one-year graduate course on Lie groups and Lie algebras. The book goes beyond the representation theory of compact Lie groups, which is the basis of many texts, and provides a carefully chosen range of material to give the student the bigger picture. The book is organized to allow different paths through the material depending on one's interests. This second edition has substantial new material, including improved discussions of underlying principles, streamlining of some proofs, and many results and topics that were not in the first edition. For compact Lie groups, the book covers the Peter–Weyl theorem, Lie algebra, conjugacy of maximal tori, the Weyl group, roots and weights, Weyl character formula, the fundamental group and more. The book continues with the study of complex analytic groups and general noncompact Lie groups, covering the Bruhat decomposition, Coxeter groups, flag varieties, symmetric spaces, Satake diagrams, embeddings of Lie groups and spin. Other topics that are treated are symmetric function theory, the representation theory of the symmetric group, Frobenius–Schur duality and GL(n) × GL(m) duality with many applications including some in random matrix theory, branching rules, Toeplitz determinants, combinatorics of tableaux, Gelfand pairs, Hecke algebras, the "philosophy of cusp forms" and the cohomology of Grassmannians. An appendix introduces the reader to the use of Sage mathematical software for Lie group computations.
Download or read book A Taste of Jordan Algebras written by Kevin McCrimmon and published by Springer Science & Business Media. This book was released on 2006-05-29 with total page 584 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the history of Jordan algebras and describes in full mathematical detail the recent structure theory for Jordan algebras of arbitrary dimension due to Efim Zel'manov. Jordan algebras crop up in many surprising settings, and find application to a variety of mathematical areas. No knowledge is required beyond standard first-year graduate algebra courses.
Download or read book Rings Modules and Algebras in Stable Homotopy Theory written by Anthony D. Elmendorf and published by American Mathematical Soc.. This book was released on 1997 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces a new point-set level approach to stable homotopy theory that has already had many applications and promises to have a lasting impact on the subject. Given the sphere spectrum $S$, the authors construct an associative, commutative, and unital smash product in a complete and cocomplete category of ``$S$-modules'' whose derived category is equivalent to the classical stable homotopy category. This construction allows for a simple and algebraically manageable definition of ``$S$-algebras'' and ``commutative $S$-algebras'' in terms of associative, or associative and commutative, products $R\wedge SR \longrightarrow R$. These notions are essentially equivalent to the earlier notions of $A {\infty $ and $E {\infty $ ring spectra, and the older notions feed naturally into the new framework to provide plentiful examples. There is an equally simple definition of $R$-modules in terms of maps $R\wedge SM\longrightarrow M$. When $R$ is commutative, the category of $R$-modules also has a
Download or read book Dirac Operators in Representation Theory written by Jing-Song Huang and published by Springer Science & Business Media. This book was released on 2007-05-27 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a comprehensive treatment of important new ideas on Dirac operators and Dirac cohomology. Using Dirac operators as a unifying theme, the authors demonstrate how some of the most important results in representation theory fit together when viewed from this perspective. The book is an excellent contribution to the mathematical literature of representation theory, and this self-contained exposition offers a systematic examination and panoramic view of the subject. The material will be of interest to researchers and graduate students in representation theory, differential geometry, and physics.
Download or read book Berkeley Lectures on P adic Geometry written by Peter Scholze and published by Princeton University Press. This book was released on 2020-05-26 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Berkeley Lectures on p-adic Geometry presents an important breakthrough in arithmetic geometry. In 2014, leading mathematician Peter Scholze delivered a series of lectures at the University of California, Berkeley, on new ideas in the theory of p-adic geometry. Building on his discovery of perfectoid spaces, Scholze introduced the concept of “diamonds,” which are to perfectoid spaces what algebraic spaces are to schemes. The introduction of diamonds, along with the development of a mixed-characteristic shtuka, set the stage for a critical advance in the discipline. In this book, Peter Scholze and Jared Weinstein show that the moduli space of mixed-characteristic shtukas is a diamond, raising the possibility of using the cohomology of such spaces to attack the Langlands conjectures for a reductive group over a p-adic field. This book follows the informal style of the original Berkeley lectures, with one chapter per lecture. It explores p-adic and perfectoid spaces before laying out the newer theory of shtukas and their moduli spaces. Points of contact with other threads of the subject, including p-divisible groups, p-adic Hodge theory, and Rapoport-Zink spaces, are thoroughly explained. Berkeley Lectures on p-adic Geometry will be a useful resource for students and scholars working in arithmetic geometry and number theory.
