Topics in varieties of group representations / Samuel M. Vovsi.

Format:

Book

Author/Creator:

Vovsi, S. M. (Samuil Mikhaĭlovich), author.

Series:

London Mathematical Society lecture note series ; 163.

London Mathematical Society lecture note series ; 163

Language:

English

Subjects (All):

Representations of groups.

Physical Description:

1 online resource (xiv, 200 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 1991.

Language Note:

English

Summary:

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.

Contents:

Cover; Haft-title; Title; Copyright; Dedication; Contents; Preface; Chapter 0. PRELIMINARIES; 0.1. Representations; 0.2. Identities and varieties; 0.3. Certain properties of varieties; 0.4. Changing the ground ring; 0.5. The free group algebra; Chapter 1. STABLE VARIETIES AND HOMOGENEITY; 1.1. Finiteness properties; 1.2. Homogeneous varieties; 1.3. Connections with varieties of associative algebras; 1.4. Stable varieties of class 4; 1.5. A stable nonhomogeneous variety; 1.6. Stability of unipotent varieties; Chapter 2. LOCALLY FINITE-DIMENSIONAL VARIETIES; 2.1. Basic notions and properties

2.2. Characterization of locally finite and locally finite-dimensional varieties2.3. The order functions; 2.4. Critical representations; 2.5. Critical representations and irreducibility; Chapter 3. IDENTITIES OF FINITE AND STABLE-BY-FINITE REPRESENTATIONS; 3.1. Ordinary representations of finite groups; 3.2. Several auxiliary results; 3.3. Bounds for the orders of critical representations; 3.4. Identities of stable-by-finite representations; 3.5. Corollaries and related results; Chapter 4. FURTHER TOPICS; 4.1. Multilinear identities and partial linearizations

4.2. Identities of representations of abelian groups and related results4.3. Multiplication of pure varieties; 4.4. Intersection of pure varieties; 4.5. Some applications: an overview; References; Index

Notes:

Title from publisher's bibliographic system (viewed on 31 May 2016).

Includes bibliographical references and index.

ISBN:

1-139-88475-1

1-107-36670-4

1-107-37138-4

1-107-36179-6

1-107-36904-5

1-299-40445-6

1-107-36424-8

0-511-52596-6