Download or read book Integral Representation Theory written by Jaroslav Lukeš and published by Walter de Gruyter. This book was released on 2010 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents the state of the art of convexity, with an emphasis to integral representation. The exposition is focused on Choquet's theory of function spaces with a link to compact convex sets. An important feature of the book is an interplay between various mathematical subjects, such as functional analysis, measure theory, descriptive set theory, Banach spaces theory and potential theory. A substantial part of the material is of fairly recent origin and many results appear in the book form for the first time. The text is self-contained and covers a wide range of applications. From the contents: Geometry of convex sets Choquet theory of function spaces Affine functions on compact convex sets Perfect classes of functions and representation of affine functions Simplicial function spaces Choquet's theory of function cones Topologies on boundaries Several results on function spaces and compact convex sets Continuous and measurable selectors Construction of function spaces Function spaces in potential theory and Dirichlet problem Applications
Download or read book Integral Representations written by I. Reiner and published by Springer. This book was released on 2006-11-15 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Integral Geometry and Representation Theory written by I. M. Gel'fand and published by Academic Press. This book was released on 2014-05-12 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: Generalized Functions, Volume 5: Integral Geometry and Representation Theory is devoted to the theory of representations, focusing on the group of two-dimensional complex matrices of determinant one. This book emphasizes that the theory of representations is a good example of the use of algebraic and geometric methods in functional analysis, in which transformations are performed not on the points of a space, but on the functions defined on it. The topics discussed include Radon transform on a real affine space, integral transforms in the complex domain, and representations of the group of complex unimodular matrices in two dimensions. The properties of the Fourier transform on G, integral geometry in a space of constant curvature, harmonic analysis on spaces homogeneous with respect to the Lorentz Group, and invariance under translation and dilation are also described. This volume is suitable for mathematicians, specialists, and students learning integral geometry and representation theory.
Download or read book Characters of Groups and Lattices over Orders written by Alexander Zimmermann and published by Walter de Gruyter GmbH & Co KG. This book was released on 2022-01-19 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the fi rst textbook leading coherently from classical character theory to the theory of lattices over orders and integral representations of fi nite groups. Character theory is developed in a highly pedagogical way including many examples and exercises covering at once the fi rst defi nitions up to Clifford theory, Brauer’s induction theorem and the splitting fi eld theorem, as well as self-dual simple modules allowing bilinear forms. This latter part is done step by step using the approach given by Sin and Willems. Dirichlet characters and Dirichlet’s result on primes in arithmetic progressions are given as an application. Examples of integral representations of fi nite groups are already detailed at a quite early stage where appropriate, so that the more systematic treatment of lattices over orders is natural. After that, the necessary number theory and homological algebra is developed as far as needed. Maximal as well as hereditary orders are introduced and the Auslander- Buchsbaum theorem is proved. The Jordan-Zassenhaus theorem on the fi niteness of lattices in a given vector space is fully proved. Then the development and properties of class groups of orders is a fi rst focus. As a further highlight Swan’s example of a stably free but not free ideal over the integral group ring of the generalised quaternion group of order 32 is developed in great detail. A student friendly introduction to ordinary representation theory Many examples and exercises, including solutions for some of them, make the book well suited for self-study Leads coherently from ordinary character theory to the integral representation theory of lattices over orders Several topics appear for the fi rst time in a textbook, such as Sin-Willems’ approach to self-dual simple modules and Swan‘s example of a stably free non free ideal.
Download or read book Quaternion Algebras written by John Voight and published by Springer Nature. This book was released on 2021-06-28 with total page 877 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access textbook presents a comprehensive treatment of the arithmetic theory of quaternion algebras and orders, a subject with applications in diverse areas of mathematics. Written to be accessible and approachable to the graduate student reader, this text collects and synthesizes results from across the literature. Numerous pathways offer explorations in many different directions, while the unified treatment makes this book an essential reference for students and researchers alike. Divided into five parts, the book begins with a basic introduction to the noncommutative algebra underlying the theory of quaternion algebras over fields, including the relationship to quadratic forms. An in-depth exploration of the arithmetic of quaternion algebras and orders follows. The third part considers analytic aspects, starting with zeta functions and then passing to an idelic approach, offering a pathway from local to global that includes strong approximation. Applications of unit groups of quaternion orders to hyperbolic geometry and low-dimensional topology follow, relating geometric and topological properties to arithmetic invariants. Arithmetic geometry completes the volume, including quaternionic aspects of modular forms, supersingular elliptic curves, and the moduli of QM abelian surfaces. Quaternion Algebras encompasses a vast wealth of knowledge at the intersection of many fields. Graduate students interested in algebra, geometry, and number theory will appreciate the many avenues and connections to be explored. Instructors will find numerous options for constructing introductory and advanced courses, while researchers will value the all-embracing treatment. Readers are assumed to have some familiarity with algebraic number theory and commutative algebra, as well as the fundamentals of linear algebra, topology, and complex analysis. More advanced topics call upon additional background, as noted, though essential concepts and motivation are recapped throughout.
Download or read book Representation Theory of Finite Groups written by Martin Burrow and published by Academic Press. This book was released on 2014-05-10 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: Representation Theory of Finite Groups is a five chapter text that covers the standard material of representation theory. This book starts with an overview of the basic concepts of the subject, including group characters, representation modules, and the rectangular representation. The succeeding chapters describe the features of representation theory of rings with identity and finite groups. These topics are followed by a discussion of some of the application of the theory of characters, along with some classical theorems. The last chapter deals with the construction of irreducible representations of groups. This book will be of great value to graduate students who wish to acquire some knowledge of representation theory.
Download or read book Integral Representation and the Computation of Combinatorial Sums written by G. P. Egorychev and published by American Mathematical Soc.. This book was released on 1984-12-31 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph should be of interest to a broad spectrum of readers: specialists in discrete and continuous mathematics, physicists, engineers, and others interested in computing sums and applying complex analysis in discrete mathematics. It contains investigations on the problem of finding integral representations for and computing finite and infinite sums (generating functions); these arise in practice in combinatorial analysis, the theory of algorithms and programming on a computer, probability theory, group theory, and function theory, as well as in physics and other areas of knowledge. A general approach is presented for computing sums and other expressions in closed form by reducing them to one-dimensional and multiple integrals, most often to contour integrals.
Download or read book A Course in Finite Group Representation Theory written by Peter Webb and published by Cambridge University Press. This book was released on 2016-08-19 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: This graduate-level text provides a thorough grounding in the representation theory of finite groups over fields and rings. The book provides a balanced and comprehensive account of the subject, detailing the methods needed to analyze representations that arise in many areas of mathematics. Key topics include the construction and use of character tables, the role of induction and restriction, projective and simple modules for group algebras, indecomposable representations, Brauer characters, and block theory. This classroom-tested text provides motivation through a large number of worked examples, with exercises at the end of each chapter that test the reader's knowledge, provide further examples and practice, and include results not proven in the text. Prerequisites include a graduate course in abstract algebra, and familiarity with the properties of groups, rings, field extensions, and linear algebra.
Download or read book Holomorphic Functions and Integral Representations in Several Complex Variables written by R. Michael Range and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of this book is Complex Analysis in Several Variables. This text begins at an elementary level with standard local results, followed by a thorough discussion of the various fundamental concepts of "complex convexity" related to the remarkable extension properties of holomorphic functions in more than one variable. It then continues with a comprehensive introduction to integral representations, and concludes with complete proofs of substantial global results on domains of holomorphy and on strictly pseudoconvex domains inC", including, for example, C. Fefferman's famous Mapping Theorem. The most important new feature of this book is the systematic inclusion of many of the developments of the last 20 years which centered around integral representations and estimates for the Cauchy-Riemann equations. In particu lar, integral representations are the principal tool used to develop the global theory, in contrast to many earlier books on the subject which involved methods from commutative algebra and sheaf theory, and/or partial differ ential equations. I believe that this approach offers several advantages: (1) it uses the several variable version of tools familiar to the analyst in one complex variable, and therefore helps to bridge the often perceived gap between com plex analysis in one and in several variables; (2) it leads quite directly to deep global results without introducing a lot of new machinery; and (3) concrete integral representations lend themselves to estimations, therefore opening the door to applications not accessible by the earlier methods.
Download or read book Representation Theory Complex Analysis and Integral Geometry written by Bernhard Krötz and published by Springer Science & Business Media. This book was released on 2011-12-13 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume targets graduate students and researchers in the fields of representation theory, automorphic forms, Hecke algebras, harmonic analysis, number theory.
Download or read book Representation Theory and Noncommutative Harmonic Analysis II written by A.A. Kirillov and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two surveys introducing readers to the subjects of harmonic analysis on semi-simple spaces and group theoretical methods, and preparing them for the study of more specialised literature. This book will be very useful to students and researchers in mathematics, theoretical physics and those chemists dealing with quantum systems.
Download or read book Representation Theory of Finite Groups and Associative Algebras written by Charles W. Curtis and published by American Mathematical Soc.. This book was released on 2006 with total page 714 pages. Available in PDF, EPUB and Kindle. Book excerpt: Provides an introduction to various aspects of the representation theory of finite groups. This book covers such topics as general non-commutative algebras, Frobenius algebras, representations over non-algebraically closed fields and fields of non-zero characteristic, and integral representations.
Download or read book Solution of a Non Domestic Tame Classification Problem from Integral Representation Theory of Finite Groups Lambda RC 3 v 3 4 written by Ernst Dieterich and published by American Mathematical Soc.. This book was released on 1991 with total page 165 pages. Available in PDF, EPUB and Kindle. Book excerpt: Suppose [italic capital]R be a complete discrete valuation ring with exponential valuation [lowercase Greek]Nu, and let [italic capital]G be a finite [italic]p-group. In studying the representation type (finite, tame or wild) of the group ring [italic capital]RG, the last open problem was the case where [italic capital]G = [italic capital]C3 and [lowercase Greek]Nu(3) = 4. Here it is shown that in this group ring is tame (non-domestic and of finite growth), by way of classifying all indecomposable representations of [italic capital]C3 in [italic capital]R when [lowercase Greek]Nu(3) = 4.
Download or read book Linear Analysis and Representation Theory written by Steven A. Gaal and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 701 pages. Available in PDF, EPUB and Kindle. Book excerpt: In an age when more and more items. are made to be quickly disposable or soon become obsolete due to either progress or other man caused reasons it seems almost anachronistic to write a book in the classical sense. A mathematics book becomes an indespensible companion, if it is worthy of such a relation, not by being rapidly read from cover to cover but by frequent browsing, consultation and other occasional use. While trying to create such a work I tried not to be encyclopedic but rather select only those parts of each chosen topic which I could present clearly and accurately in a formulation which is likely to last. The material I chose is all mathematics which is interesting and important both for the mathematician and to a large extent also for the mathematical physicist. I regret that at present I could not give a similar account on direct integrals and the representation theory of certain classes of Lie groups. I carefully kept the level of presentation throughout the whole book as uniform as possible. Certain introductory sections are kept shorter and are perhaps slightly more detailed in order to help the newcomer prog ress with it at the same rate as the more experienced person is going to proceed with his study of the details.
Download or read book Representation Theory of Lie Groups written by M. F. Atiyah and published by Cambridge University Press. This book was released on 1979 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1977 a symposium was held in Oxford to introduce Lie groups and their representations to non-specialists.
Download or read book Introduction to Representation Theory written by Pavel I. Etingof and published by American Mathematical Soc.. This book was released on 2011 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a ``holistic'' introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra.
Download or read book Introduction to the Representation Theory of Algebras written by Michael Barot and published by Springer. This book was released on 2014-12-29 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a general introduction to the theory of representations of algebras. It starts with examples of classification problems of matrices under linear transformations, explaining the three common setups: representation of quivers, modules over algebras and additive functors over certain categories. The main part is devoted to (i) module categories, presenting the unicity of the decomposition into indecomposable modules, the Auslander–Reiten theory and the technique of knitting; (ii) the use of combinatorial tools such as dimension vectors and integral quadratic forms; and (iii) deeper theorems such as Gabriel‘s Theorem, the trichotomy and the Theorem of Kac – all accompanied by further examples. Each section includes exercises to facilitate understanding. By keeping the proofs as basic and comprehensible as possible and introducing the three languages at the beginning, this book is suitable for readers from the advanced undergraduate level onwards and enables them to consult related, specific research articles.
