Topics in Varieties of Group Representations [Paperback]

This book is devoted to the theory of group representations and is intended for a broad audience of researchers and graduate students.Devoted to the theory of group representations, a promising area of modern algebra, this textbook provides a detailed exposition of several central topics in the field, leading to the most current advances and developments.Devoted to the theory of group representations, a promising area of modern algebra, this textbook provides a detailed exposition of several central topics in the field, leading to the most current advances and developments.The present book is devoted to one of the newest branches of variety theory: varieties of group representations. In addition to its intrinsic value, it has numerous connections with varieties of groups, rings and Lie algebras, polynomial identities, group rings, etc., and provides results, methods and ideas that are of interest to a broad algebraic audience. The book presents a clear and detailed exposition of several central topics in the field, leading from initial definitions and problems to the most current advances and developments. Among the topics treated are stable and unipotent varieties, locally finite-dimensional varieties, the finite basis problem, connections with varieties of groups and associative algebras and their applications.Preliminaries; 1. Stable varieties and homogeneity; 2. Locally finite-dimensional varieties; 3. Identities of finite and stable bifinite representations; Further topics. The book presents to non-Russian readers a theory that has been developed almost entirely in the former Soviet Union. It is clear and hardly suffers at all from the fact that English is not the author's first language....The fact is that the book is well organized and easy to understand. Peter M. Neumann, Bulletin of the American Mathematical Society