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Author : D. J. Benson
Publisher : Cambridge University Press
Page : 260 pages
File Size : 48,5 Mb
Release : 1998-06-18
Category : Mathematics
ISBN : 0521636531
An introduction to modern developments in the representation theory of finite groups and associative algebras.
Author : D. J. Benson
Publisher : Cambridge University Press
Page : 296 pages
File Size : 45,9 Mb
Release : 1991-08-22
Category : Mathematics
ISBN : 0521636523
A further introduction to modern developments in the representation theory of finite groups and associative algebras.
Author : David J. Benson
Publisher : Unknown
Page : 279 pages
File Size : 43,5 Mb
Release : 1991
Category : Homology theory
ISBN : OCLC:726824774
Author : D. J. Benson
Publisher : Cambridge University Press
Page : 260 pages
File Size : 49,9 Mb
Release : 1991-03-21
Category : Mathematics
ISBN : 0521361346
This is the first of two volumes providing an introduction to modern developments in the representation theory of finite groups and associative algebras, which have transformed the subject into a study of categories of modules. Thus, Dr. Benson's unique perspective in this book incorporates homological algebra and the theory of representations of finite-dimensional algebras. This volume is primarily concerned with the exposition of the necessary background material, and the heart of the discussion is a lengthy introduction to the (Auslander-Reiten) representation theory of finite dimensional algebras, in which the techniques of quivers with relations and almost-split sequences are discussed in some detail.
Author : David J. Benson
Publisher : Unknown
Page : 279 pages
File Size : 51,6 Mb
Release : 1991
Category : Homology theory
ISBN : OCLC:726824774
Author : Armand Borel,Nolan R. Wallach
Publisher : American Mathematical Soc.
Page : 282 pages
File Size : 52,5 Mb
Release : 2013-11-21
Category : Mathematics
ISBN : 9781470412258
It has been nearly twenty years since the first edition of this work. In the intervening years, there has been immense progress in the use of homological algebra to construct admissible representations and in the study of arithmetic groups. This second edition is a corrected and expanded version of the original, which was an important catalyst in the expansion of the field. Besides the fundamental material on cohomology and discrete subgroups present in the first edition, this edition also contains expositions of some of the most important developments of the last two decades.
Author : Sarah J. Witherspoon
Publisher : American Mathematical Society
Page : 265 pages
File Size : 55,5 Mb
Release : 2020-06-30
Category : Mathematics
ISBN : 9781470462864
This book gives a thorough and self-contained introduction to the theory of Hochschild cohomology for algebras and includes many examples and exercises. The book then explores Hochschild cohomology as a Gerstenhaber algebra in detail, the notions of smoothness and duality, algebraic deformation theory, infinity structures, support varieties, and connections to Hopf algebra cohomology. Useful homological algebra background is provided in an appendix. The book is designed both as an introduction for advanced graduate students and as a resource for mathematicians who use Hochschild cohomology in their work.
Author : Jon F. Carlson,L. Townsley,Luís Valero-Elizondo,Mucheng Zhang
Publisher : Springer Science & Business Media
Page : 782 pages
File Size : 45,6 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9789401702157
Group cohomology has a rich history that goes back a century or more. Its origins are rooted in investigations of group theory and num ber theory, and it grew into an integral component of algebraic topology. In the last thirty years, group cohomology has developed a powerful con nection with finite group representations. Unlike the early applications which were primarily concerned with cohomology in low degrees, the in teractions with representation theory involve cohomology rings and the geometry of spectra over these rings. It is this connection to represen tation theory that we take as our primary motivation for this book. The book consists of two separate pieces. Chronologically, the first part was the computer calculations of the mod-2 cohomology rings of the groups whose orders divide 64. The ideas and the programs for the calculations were developed over the last 10 years. Several new features were added over the course of that time. We had originally planned to include only a brief introduction to the calculations. However, we were persuaded to produce a more substantial text that would include in greater detail the concepts that are the subject of the calculations and are the source of some of the motivating conjectures for the com putations. We have gathered together many of the results and ideas that are the focus of the calculations from throughout the mathematical literature.
Author : Kenneth S. Brown
Publisher : Springer Science & Business Media
Page : 318 pages
File Size : 41,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468493276
Aimed at second year graduate students, this text introduces them to cohomology theory (involving a rich interplay between algebra and topology) with a minimum of prerequisites. No homological algebra is assumed beyond what is normally learned in a first course in algebraic topology, and the basics of the subject, as well as exercises, are given prior to discussion of more specialized topics.
Author : Henning Krause
Publisher : Cambridge University Press
Page : 517 pages
File Size : 48,8 Mb
Release : 2021-11-18
Category : Mathematics
ISBN : 9781108838894
This book for advanced graduate students and researchers discusses representations of associative algebras and their homological theory.
Author : D. Benson
Publisher : Springer
Page : 246 pages
File Size : 45,7 Mb
Release : 2008-07-22
Category : Mathematics
ISBN : 9783540389408
This reprint of a 1983 Yale graduate course makes results in modular representation theory accessible to an audience ranging from second-year graduate students to established mathematicians. Following a review of background material, the lectures examine three closely connected topics in modular representation theory of finite groups: representations rings; almost split sequences and the Auslander-Reiten quiver; and complexity and cohomology varieties, which has become a major theme in representation theory.
Author : Anthony W. Knapp,David A. Vogan Jr.
Publisher : Princeton University Press
Page : 968 pages
File Size : 52,7 Mb
Release : 2016-06-02
Category : Mathematics
ISBN : 9781400883936
This book offers a systematic treatment--the first in book form--of the development and use of cohomological induction to construct unitary representations. George Mackey introduced induction in 1950 as a real analysis construction for passing from a unitary representation of a closed subgroup of a locally compact group to a unitary representation of the whole group. Later a parallel construction using complex analysis and its associated co-homology theories grew up as a result of work by Borel, Weil, Harish-Chandra, Bott, Langlands, Kostant, and Schmid. Cohomological induction, introduced by Zuckerman, is an algebraic analog that is technically more manageable than the complex-analysis construction and leads to a large repertory of irreducible unitary representations of reductive Lie groups. The book, which is accessible to students beyond the first year of graduate school, will interest mathematicians and physicists who want to learn about and take advantage of the algebraic side of the representation theory of Lie groups. Cohomological Induction and Unitary Representations develops the necessary background in representation theory and includes an introductory chapter of motivation, a thorough treatment of the "translation principle," and four appendices on algebra and analysis.
Author : Alexander Zimmermann
Publisher : Springer
Page : 720 pages
File Size : 45,9 Mb
Release : 2014-08-15
Category : Mathematics
ISBN : 9783319079684
Introducing the representation theory of groups and finite dimensional algebras, first studying basic non-commutative ring theory, this book covers the necessary background on elementary homological algebra and representations of groups up to block theory. It further discusses vertices, defect groups, Green and Brauer correspondences and Clifford theory. Whenever possible the statements are presented in a general setting for more general algebras, such as symmetric finite dimensional algebras over a field. Then, abelian and derived categories are introduced in detail and are used to explain stable module categories, as well as derived categories and their main invariants and links between them. Group theoretical applications of these theories are given – such as the structure of blocks of cyclic defect groups – whenever appropriate. Overall, many methods from the representation theory of algebras are introduced. Representation Theory assumes only the most basic knowledge of linear algebra, groups, rings and fields and guides the reader in the use of categorical equivalences in the representation theory of groups and algebras. As the book is based on lectures, it will be accessible to any graduate student in algebra and can be used for self-study as well as for classroom use.
Author : Jean-Pierre Serre
Publisher : CRC Press
Page : 203 pages
File Size : 46,8 Mb
Release : 1997-11-15
Category : Mathematics
ISBN : 9781439863862
This classic book contains an introduction to systems of l-adic representations, a topic of great importance in number theory and algebraic geometry, as reflected by the spectacular recent developments on the Taniyama-Weil conjecture and Fermat's Last Theorem. The initial chapters are devoted to the Abelian case (complex multiplication), where one
Author : Alejandro Adem,Representations Summer Research Institute on Cohomology
Publisher : American Mathematical Soc.
Page : 549 pages
File Size : 44,6 Mb
Release : 1998
Category : Finite groups
ISBN : 9780821806586
This volume combines contributions in topology and representation theory that reflect the increasingly vigorous interactions between these areas. Topics such as group theory, homotopy theory, cohomology of groups, and modular representations are covered. All papers have been carefully refereed and offer lasting value.
