Representations Of Finite Groups Local Cohomology And Support
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Representations Of Finite Groups Local Cohomology And Support
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Author : David J. Benson
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-15
Representations Of Finite Groups Local Cohomology And Support written by David J. Benson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-15 with Mathematics categories.
The seminar focuses on a recent solution, by the authors, of a long standing problem concerning the stable module category (of not necessarily finite dimensional representations) of a finite group. The proof draws on ideas from commutative algebra, cohomology of groups, and stable homotopy theory. The unifying theme is a notion of support which provides a geometric approach for studying various algebraic structures. The prototype for this has been Daniel Quillen’s description of the algebraic variety corresponding to the cohomology ring of a finite group, based on which Jon Carlson introduced support varieties for modular representations. This has made it possible to apply methods of algebraic geometry to obtain representation theoretic information. Their work has inspired the development of analogous theories in various contexts, notably modules over commutative complete intersection rings and over cocommutative Hopf algebras. One of the threads in this development has been the classification of thick or localizing subcategories of various triangulated categories of representations. This story started with Mike Hopkins’ classification of thick subcategories of the perfect complexes over a commutative Noetherian ring, followed by a classification of localizing subcategories of its full derived category, due to Amnon Neeman. The authors have been developing an approach to address such classification problems, based on a construction of local cohomology functors and support for triangulated categories with ring of operators. The book serves as an introduction to this circle of ideas.
Cohomology Rings Of Finite Groups
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Author : Jon F. Carlson
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Cohomology Rings Of Finite Groups written by Jon F. Carlson and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
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.
Projective Representations Of Finite Groups
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Author : Gregory Karpilovsky
language : en
Publisher:
Release Date : 1985
Projective Representations Of Finite Groups written by Gregory Karpilovsky and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Mathematics categories.
This book presents a systematic account of this topic, from the classical foundations established by Schur 80 years ago to current advances and developments in the field. This work focuses on general methods and builds theory solidly on the study of modules over twisted group algebras, and provides a wide range of skill-sharpening mathematical techniques applicable to this subject. Offers an understanding of projective representations of finite groups for algebraists, number theorists, mathematical researchers studying modern algebra, and theoretical physicists.
Finite And Locally Finite Groups
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Author : B. Hartley
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Finite And Locally Finite Groups written by B. Hartley and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This volume contains the proceedings of the NATO Advanced Study Institute on Finite and Locally Finite Groups held in Istanbul, Turkey, 14-27 August 1994, at which there were about 90 participants from some 16 different countries. The ASI received generous financial support from the Scientific Affairs Division of NATO. INTRODUCTION A locally finite group is a group in which every finite set of elements is contained in a finite subgroup. The study of locally finite groups began with Schur's result that a periodic linear group is, in fact, locally finite. The simple locally finite groups are of particular interest. In view of the classification of the finite simple groups and advances in representation theory, it is natural to pursue classification theorems for simple locally finite groups. This was one of the central themes of the Istanbul conference and significant progress is reported herein. The theory of simple locally finite groups intersects many areas of group theory and representation theory, so this served as a focus for several articles in the volume. Every simple locally finite group has what is known as a Kegel cover. This is a collection of pairs {(G , Ni) liE I}, where I is an index set, each group Gi is finite, i Ni
The Arcata Conference On Representations Of Finite Groups Part 1
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Author : Paul Fong
language : en
Publisher: American Mathematical Soc.
Release Date : 1987
The Arcata Conference On Representations Of Finite Groups Part 1 written by Paul Fong and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Mathematics categories.
The papers in these proceedings of the 1986 Arcata Summer Institute bear witness to the extraordinarily vital and intense research in the representation theory of finite groups. The confluence of diverse mathematical disciplines has brought forth work of great scope and depth. Particularly striking is the influence of algebraic geometry and cohomology theory in the modular representation theory and the character theory of reductive groups over finite fields, and in the general modular representation theory of finite groups. The continuing developments in block theory and the general character theory of finite groups is noteworthy. The expository and research aspects of the Summer Institute are well represented by these papers.
Modular Representations Of Finite Groups Of Lie Type
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Author : James E. Humphreys
language : en
Publisher: Cambridge University Press
Release Date : 2006
Modular Representations Of Finite Groups Of Lie Type written by James E. Humphreys and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
A comprehensive treatment of the representation theory of finite groups of Lie type over a field of the defining prime characteristic.
The Connective K Theory Of Finite Groups
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Author : Robert Ray Bruner
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
The Connective K Theory Of Finite Groups written by Robert Ray Bruner and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
Includes a paper that deals the connective K homology and cohomology of finite groups $G$. This title uses the methods of algebraic geometry to study the ring $ku DEGREES*(BG)$ where $ku$ denotes connective complex K-theory. It describes the variety in terms of the category of abelian $p$-subgroups of $G$ for primes $p$ dividing the group
Cohomology Rings Of Finite Groups
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Author : Jon Carlson
language : en
Publisher:
Release Date : 2014-01-15
Cohomology Rings Of Finite Groups written by Jon Carlson and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Cohomology Of Finite Groups
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Author : Alejandro Adem
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Cohomology Of Finite Groups written by Alejandro Adem and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
The cohomology of groups has, since its beginnings in the 1920s and 1930s, been the stage for significant interaction between algebra and topology and has led to the creation of important new fields in mathematics, like homological algebra and algebraic K-theory. This is the first book to deal comprehensively with the cohomology of finite groups: it introduces the most important and useful algebraic and topological techniques, and describes the interplay of the subject with those of homotopy theory, representation theory and group actions. The combination of theory and examples, together with the techniques for computing the cohomology of important classes of groups including symmetric groups, alternating groups, finite groups of Lie type, and some of the sporadic simple groups, enable readers to acquire an in-depth understanding of group cohomology and its extensive applications.
Representation Theory Of Finite Groups
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Author : Martin Burrow
language : en
Publisher: Courier Corporation
Release Date : 1993-01-01
Representation Theory Of Finite Groups written by Martin Burrow and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-01-01 with Mathematics categories.
Concise, graduate-level exposition of the theory of finite groups, including the theory of modular representations. Topics include representation theory of rings with identity, representation theory of finite groups, applications of the theory of characters, construction of irreducible representations and modular representations. Rudiments of linear algebra and knowledge of group theory helpful prerequisites. Exercises. Bibliography. Appendix. 1965 edition.