Representations Of Finite Groups Local Cohomology And Support

Author : David J. Benson,Srikanth Iyengar,Henning Krause
Publisher : Springer Science & Business Media
Page : 115 pages
File Size : 49,9 Mb
Release : 2011-11-15
Category : Mathematics
ISBN : 9783034802604

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Representations of Finite Groups: Local Cohomology and Support by David J. Benson,Srikanth Iyengar,Henning Krause Pdf

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.

Author : Jon F. Carlson,L. Townsley,Luís Valero-Elizondo,Mucheng Zhang
Publisher : Springer Science & Business Media
Page : 782 pages
File Size : 50,7 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9789401702157

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Cohomology Rings of Finite Groups by Jon F. Carlson,L. Townsley,Luís Valero-Elizondo,Mucheng Zhang Pdf

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 : Gregory Karpilovsky
Publisher : Unknown
Page : 672 pages
File Size : 51,9 Mb
Release : 1985
Category : Mathematics
ISBN : UOM:39015014357761

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Projective Representations of Finite Groups by Gregory Karpilovsky Pdf

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.

Author : Calif.) Arcata Conference on Representations of Finite Groups (1986 : Arcata,Paul Fong,Conference on Representations of Finite Groups,American Mathematical Society
Publisher : American Mathematical Soc.
Page : 552 pages
File Size : 42,9 Mb
Release : 1987
Category : Mathematics
ISBN : 9780821814789

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The Arcata Conference on Representations of Finite Groups, Part 2 by Calif.) Arcata Conference on Representations of Finite Groups (1986 : Arcata,Paul Fong,Conference on Representations of Finite Groups,American Mathematical Society Pdf

Author : B. Hartley,G.M. Seitz,A.V. Borovik,R.M. Bryant
Publisher : Springer Science & Business Media
Page : 469 pages
File Size : 46,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401103299

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Finite and Locally Finite Groups by B. Hartley,G.M. Seitz,A.V. Borovik,R.M. Bryant Pdf

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

Author : D. J. Benson
Publisher : Cambridge University Press
Page : 296 pages
File Size : 53,7 Mb
Release : 1991-08-22
Category : Mathematics
ISBN : 0521636523

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Representations and Cohomology: Volume 2, Cohomology of Groups and Modules by D. J. Benson Pdf

A further introduction to modern developments in the representation theory of finite groups and associative algebras.

Author : James E. Humphreys
Publisher : Cambridge University Press
Page : 260 pages
File Size : 48,7 Mb
Release : 2006
Category : Mathematics
ISBN : 0521674549

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Modular Representations of Finite Groups of Lie Type by James E. Humphreys Pdf

A comprehensive treatment of the representation theory of finite groups of Lie type over a field of the defining prime characteristic.

Author : Martin Burrow
Publisher : Courier Corporation
Page : 210 pages
File Size : 42,9 Mb
Release : 1993-01-01
Category : Mathematics
ISBN : 9780486674872

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Representation Theory of Finite Groups by Martin Burrow Pdf

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.

Author : Haynes Miller
Publisher : CRC Press
Page : 1043 pages
File Size : 52,8 Mb
Release : 2020-01-23
Category : Mathematics
ISBN : 9781351251600

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Handbook of Homotopy Theory by Haynes Miller Pdf

The Handbook of Homotopy Theory provides a panoramic view of an active area in mathematics that is currently seeing dramatic solutions to long-standing open problems, and is proving itself of increasing importance across many other mathematical disciplines. The origins of the subject date back to work of Henri Poincaré and Heinz Hopf in the early 20th century, but it has seen enormous progress in the 21st century. A highlight of this volume is an introduction to and diverse applications of the newly established foundational theory of ¥ -categories. The coverage is vast, ranging from axiomatic to applied, from foundational to computational, and includes surveys of applications both geometric and algebraic. The contributors are among the most active and creative researchers in the field. The 22 chapters by 31 contributors are designed to address novices, as well as established mathematicians, interested in learning the state of the art in this field, whose methods are of increasing importance in many other areas.

Author : Jon Carlson,L. Townsley,Luis Valero-Elizondo
Publisher : Unknown
Page : 796 pages
File Size : 47,9 Mb
Release : 2014-01-15
Category : Electronic
ISBN : 9401702160

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Cohomology Rings of Finite Groups by Jon Carlson,L. Townsley,Luis Valero-Elizondo Pdf

Author : Andrzej Skowroński,Kunio Yamagata
Publisher : European Mathematical Society
Page : 744 pages
File Size : 46,8 Mb
Release : 2011
Category : Algebra
ISBN : 3037191015

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Representations of Algebras and Related Topics by Andrzej Skowroński,Kunio Yamagata Pdf

This book, which explores recent trends in the representation theory of algebras and its exciting interaction with geometry, topology, commutative algebra, Lie algebras, combinatorics, quantum algebras, and theoretical field, is conceived as a handbook to provide easy access to the present state of knowledge and stimulate further development. The many topics discussed include quivers, quivers with potential, bound quiver algebras, Jacobian algebras, cluster algebras and categories, Calabi-Yau algebras and categories, triangulated and derived categories, and quantum loop algebras. This book consists of thirteen self-contained expository survey and research articles and is addressed to researchers and graduate students in algebra as well as a broader mathematical community. The articles contain a large number of examples and open problems and give new perspectives for research in the field.

Author : Chat Yin Ho,Peter Sin,Pham Huu Tiep,Alexandre Turull
Publisher : Walter de Gruyter
Page : 434 pages
File Size : 47,7 Mb
Release : 2008-08-22
Category : Mathematics
ISBN : 9783110198126

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Finite Groups 2003 by Chat Yin Ho,Peter Sin,Pham Huu Tiep,Alexandre Turull Pdf

This is a volume of research articles related to finite groups. Topics covered include the classification of finite simple groups, the theory of p-groups, cohomology of groups, representation theory and the theory of buildings and geometries. As well as more than twenty original papers on the latest developments, which will be of great interest to specialists, the volume contains several expository articles, from which students and non-experts can learn about the present state of knowledge and promising directions for further research. The Finite Groups 2003 conference was held in honor of John Thompson. The profound influence of his fundamental contributions is clearly visible in this collection of papers dedicated to him.

Author : Robert Ray Bruner,John Patrick Campbell Greenlees
Publisher : American Mathematical Soc.
Page : 144 pages
File Size : 44,8 Mb
Release : 2003
Category : Algebraic topology
ISBN : 9780821833667

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The Connective K-Theory of Finite Groups by Robert Ray Bruner,John Patrick Campbell Greenlees Pdf

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

Author : Alejandro Adem,R.James Milgram
Publisher : Springer Science & Business Media
Page : 333 pages
File Size : 40,5 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9783662062821

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Cohomology of Finite Groups by Alejandro Adem,R.James Milgram Pdf

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.

Author : Jean-Pierre Serre
Publisher : Springer Science & Business Media
Page : 178 pages
File Size : 44,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781468494587

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Linear Representations of Finite Groups by Jean-Pierre Serre Pdf

This book consists of three parts, rather different in level and purpose. The first part was originally written for quantum chemists. It describes the correspondence, due to Frobenius, between linear representations and characters. The second part is a course given in 1966 to second-year students of l’Ecole Normale. It completes in a certain sense the first part. The third part is an introduction to Brauer Theory.