Download or read book Representations and Cohomology ICM Edition Volume 2 Cohomology of Groups and Modules written by D. J. Benson and published by . This book was released on 2010-07-23 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Representations and Cohomology Volume 2 Cohomology of Groups and Modules written by D. J. Benson and published by Cambridge University Press. This book was released on 1991-08-22 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: A further introduction to modern developments in the representation theory of finite groups and associative algebras.
Download or read book Representations and Cohomology Volume 1 Basic Representation Theory of Finite Groups and Associative Algebras written by D. J. Benson and published by Cambridge University Press. This book was released on 1998-06-18 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to modern developments in the representation theory of finite groups and associative algebras.
Download or read book Representations and Cohomology written by David J. Benson and published by . This book was released on 1991 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Representations and Cohomology Volume 1 Basic Representation Theory of Finite Groups and Associative Algebras written by D. J. Benson and published by Cambridge University Press. This book was released on 1991-03-21 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Cohomology Rings of Finite Groups written by Jon F. Carlson and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 782 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Cohomology of Finite Groups written by Alejandro Adem and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 333 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Representations of Finite Groups Local Cohomology and Support written by David J. Benson and published by Springer Science & Business Media. This book was released on 2011-11-15 with total page 115 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Cohomology of Groups written by and published by Academic Press. This book was released on 1969 with total page 289 pages. Available in PDF, EPUB and Kindle. Book excerpt: Cohomology of Groups
Download or read book Representations and Cohomology Volume 1 Basic Representation Theory of Finite Groups and Associative Algebras written by D. J. Benson and published by Cambridge University Press. This book was released on 1998-06-18 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Representations and Cohomology Volume 2 Cohomology of Groups and Modules written by D. J. Benson and published by Cambridge University Press. This book was released on 1991-08-22 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: The heart of the book is a lengthy introduction to the representation theory of finite dimensional algebras, in which the techniques of quivers with relations and almost split sequences are discussed in some detail.
Download or read book Gr bner Bases and the Computation of Group Cohomology written by David J. Green and published by Springer Science & Business Media. This book was released on 2003-11-18 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph develops the Gröbner basis methods needed to perform efficient state of the art calculations in the cohomology of finite groups. Results obtained include the first counterexample to the conjecture that the ideal of essential classes squares to zero. The context is J. F. Carlson’s minimal resolutions approach to cohomology computations.
Download or read book Cohomology of Drinfeld Modular Varieties Part 1 Geometry Counting of Points and Local Harmonic Analysis written by Gérard Laumon and published by Cambridge University Press. This book was released on 1996 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 1995, Cohomology of Drinfeld Modular Varieties aimed to provide an introduction, in two volumes, both to this subject and to the Langlands correspondence for function fields. These varieties are the analogues for function fields of the Shimura varieties over number fields. The Langlands correspondence is a conjectured link between automorphic forms and Galois representations over a global field. By analogy with the number-theoretic case, one expects to establish the conjecture for function fields by studying the cohomology of Drinfeld modular varieties, which has been done by Drinfeld himself for the rank two case. The present volume is devoted to the geometry of these varieties, and to the local harmonic analysis needed to compute their cohomology. Though the author considers only the simpler case of function rather than number fields, many important features of the number field case can be illustrated.
Download or read book Continuous Cohomology Discrete Subgroups and Representations of Reductive Groups written by Armand Borel and published by American Mathematical Soc.. This book was released on 2013-11-21 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Group Cohomology and Algebraic Cycles written by Burt Totaro and published by Cambridge University Press. This book was released on 2014-06-26 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a coherent suite of computational tools for the study of group cohomology algebraic cycles.
Download or read book Cohomology of Groups written by Kenneth S. Brown and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Modular Forms and Galois Cohomology written by Haruzo Hida and published by Cambridge University Press. This book was released on 2000-06-29 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comprehensive account of recent developments in arithmetic theory of modular forms, for graduates and researchers.
