Topics In Varieties Of Group Representations

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Topics In Varieties Of Group Representations

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Author : Samuel M. Vovsi
language : en
Publisher: Cambridge University Press
Release Date : 1991-11-28

Topics In Varieties Of Group Representations written by Samuel M. Vovsi 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 1991-11-28 with Mathematics categories.

This book is devoted to the theory of group representations, a young and promising area of modern algebra. It provides a detailed exposition of several central topics in the field, leading to the most current advances and developments. Much of the included material has never been available in book form before. It is intended for a broad audience of researchers and graduate students, working in abstract algebra and its many applications.

Topics In Varieties Of Group Representations

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Author : Samuil Mikhaĭlovich Vovsi
language : en
Publisher:
Release Date : 1992

Topics In Varieties Of Group Representations written by Samuil Mikhaĭlovich Vovsi and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Electronic books categories.

This book is devoted to the theory of group representations and is intended for a broad audience of researchers and graduate students.

Kac Moody Groups Their Flag Varieties And Representation Theory

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Author : Shrawan Kumar
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Kac Moody Groups Their Flag Varieties And Representation Theory written by Shrawan Kumar 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.

Kac-Moody Lie algebras 9 were introduced in the mid-1960s independently by V. Kac and R. Moody, generalizing the finite-dimensional semisimple Lie alge bras which we refer to as the finite case. The theory has undergone tremendous developments in various directions and connections with diverse areas abound, including mathematical physics, so much so that this theory has become a stan dard tool in mathematics. A detailed treatment of the Lie algebra aspect of the theory can be found in V. Kac's book [Kac-90l This self-contained work treats the algebro-geometric and the topological aspects of Kac-Moody theory from scratch. The emphasis is on the study of the Kac-Moody groups 9 and their flag varieties XY, including their detailed construction, and their applications to the representation theory of g. In the finite case, 9 is nothing but a semisimple Y simply-connected algebraic group and X is the flag variety 9 /Py for a parabolic subgroup p y C g.

Tits Buildings And The Model Theory Of Groups

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Author : Katrin Tent
language : en
Publisher: Cambridge University Press
Release Date : 2002-01-03

Tits Buildings And The Model Theory Of Groups written by Katrin Tent 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 2002-01-03 with Mathematics categories.

Introduction to buildings and their geometries with emphasis on model theoretic constructions, covering recent developments.

Topics In Infinite Group Theory

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Author : Benjamin Fine
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2024-11-18

Topics In Infinite Group Theory written by Benjamin Fine and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-18 with Mathematics categories.

This book gives an advanced overview of several topics in infinite group theory. It can also be considered as a rigorous introduction to combinatorial and geometric group theory. The philosophy of the book is to describe the interaction between these two important parts of infinite group theory. In this line of thought, several theorems are proved multiple times with different methods either purely combinatorial or purely geometric while others are shown by a combination of arguments from both perspectives. The first part of the book deals with Nielsen methods and introduces the reader to results and examples that are helpful to understand the following parts. The second part focuses on covering spaces and fundamental groups, including covering space proofs of group theoretic results. The third part deals with the theory of hyperbolic groups. The subjects are illustrated and described by prominent examples and an outlook on solved and unsolved problems. New edition now includes the topics on universal free groups, quasiconvex subgroups and hyperbolic groups, and also Stallings foldings and subgroups of free groups. New results on groups of F-types are added.

Representations Of Solvable Groups

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Author : Olaf Manz
language : en
Publisher: Cambridge University Press
Release Date : 1993-09-16

Representations Of Solvable Groups written by Olaf Manz 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 1993-09-16 with Mathematics categories.

Representation theory plays an important role in algebra, and in this book Manz and Wolf concentrate on that part of the theory which relates to solvable groups. The authors begin by studying modules over finite fields, which arise naturally as chief factors of solvable groups. The information obtained can then be applied to infinite modules, and in particular to character theory (ordinary and Brauer) of solvable groups. The authors include proofs of Brauer's height zero conjecture and the Alperin-McKay conjecture for solvable groups. Gluck's permutation lemma and Huppert's classification of solvable two-transive permutation groups, which are essentially results about finite modules of finite groups, play important roles in the applications and a new proof is given of the latter. Researchers into group theory, representation theory, or both, will find that this book has much to offer.

Trends In Representation Theory Of Algebras And Related Topics

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Author : Andrzej Skowroński
language : en
Publisher: European Mathematical Society
Release Date : 2008

Trends In Representation Theory Of Algebras And Related Topics written by Andrzej Skowroński and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Algebra categories.

This book is concerned with recent trends in the representation theory of algebras and its exciting interaction with geometry, topology, commutative algebra, Lie algebras, quantum groups, homological algebra, invariant theory, combinatorics, model theory and theoretical physics. The collection of articles, written by leading researchers in the field, is conceived as a sort of handbook providing easy access to the present state of knowledge and stimulating further development. The topics under discussion include diagram algebras, Brauer algebras, cellular algebras, quasi-hereditary algebras, Hall algebras, Hecke algebras, symplectic reflection algebras, Cherednik algebras, Kashiwara crystals, Fock spaces, preprojective algebras, cluster algebras, rank varieties, varieties of algebras and modules, moduli of representations of quivers, semi-invariants of quivers, Cohen-Macaulay modules, singularities, coherent sheaves, derived categories, spectral representation theory, Coxeter polynomials, Auslander-Reiten theory, Calabi-Yau triangulated categories, Poincare duality spaces, selfinjective algebras, periodic algebras, stable module categories, Hochschild cohomologies, deformations of algebras, Galois coverings of algebras, tilting theory, algebras of small homological dimensions, representation types of algebras, and model theory. This book consists of fifteen self-contained expository survey articles and is addressed to researchers and graduate students in algebra as well as a broader mathematical community. They contain a large number of open problems and give new perspectives for research in the field.

Tame Topology And O Minimal Structures

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Author : Lou Van den Dries
language : en
Publisher: Cambridge University Press
Release Date : 1998-05-07

Tame Topology And O Minimal Structures written by Lou Van den Dries 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 1998-05-07 with Mathematics categories.

These notes give a self-contained treatment of the theory of o-minimal structures from a geometric and topological viewpoint, assuming only rudimentary algebra and analysis. This book should be of interest to model theorists, analytic geometers and topologists.

Elementary Theory Of Groups And Group Rings And Related Topics

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Author : Paul Baginski
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-02-10

Elementary Theory Of Groups And Group Rings And Related Topics written by Paul Baginski and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-02-10 with Mathematics categories.

This proceedings volume documents the contributions presented at the conference held at Fairfield University and at the Graduate Center, CUNY in 2018 celebrating the New York Group Theory Seminar, in memoriam Gilbert Baumslag, and to honor Benjamin Fine and Anthony Gaglione. It includes several expert contributions by leading figures in the group theory community and provides a valuable source of information on recent research developments.

Characters And Blocks Of Finite Groups

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Author : Gabriel Navarro
language : en
Publisher: Cambridge University Press
Release Date : 1998-05-07

Characters And Blocks Of Finite Groups written by Gabriel Navarro 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 1998-05-07 with Mathematics categories.

This is a clear, accessible and up-to-date exposition of modular representation theory of finite groups from a character-theoretic viewpoint. After a short review of the necessary background material, the early chapters introduce Brauer characters and blocks and develop their basic properties. The next three chapters study and prove Brauer's first, second and third main theorems in turn. These results are then applied to prove a major application of finite groups, the Glauberman Z*-theorem. Later chapters examine Brauer characters in more detail. The relationship between blocks and normal subgroups is also explored and the modular characters and blocks in p-solvable groups are discussed. Finally, the character theory of groups with a Sylow p-subgroup of order p is studied. Each chapter concludes with a set of problems. The book is aimed at graduate students, with some previous knowledge of ordinary character theory, and researchers studying the representation theory of finite groups.