Gregory Karpilovsky's Books

Group Representations

By: Gregory Karpilovsky

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This second volume deals with projective representations and the Schur multiplier. Some further topics pertaining to projective representations will be covered in the next volume. The bibliography is extensive, leading the reader to various references for detailed discussions on the main topics as well as on related subjects.

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Page Count

919

Publisher

Elsevier

Published Date

ISBN 10

1483295095

ISBN 13

9781483295091

Symmetric and G-algebras

With Applications to Group Representations

By: Gregory Karpilovsky

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Symmetric and G-algebras

With Applications to Group Representations

By: Gregory Karpilovsky

The theory of symmetric and G-algebras has experienced a rapid growth in the last ten to fifteen years, acquiring mathematical depth and significance and leading to new insights in group representation theory. This volume provides a systematic account of the theory together with a number of applicat

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381

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Springer Science & Business Media

Published Date

ISBN 10

9400905971

ISBN 13

9789400905979

Group Identities on Units and Symmetric Units of Group Rings

By: Gregory T Lee

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Group Identities on Units and Symmetric Units of Group Rings

By: Gregory T Lee

Let FG be the group ring of a group G over a field F. Write U(FG) for the group of units of FG. It is an important problem to determine the conditions under which U(FG) satisfies a group identity. In the mid 1990s, a conjecture of Hartley was verified, namely, if U(FG) satisfies a group identity, and G is torsion, then FG satisfies a polynomial identity. Necessary and sufficient conditions for U(FG) to satisfy a group identity soon followed. Since the late 1990s, many papers have been devoted to the study of the symmetric units; that is, those units u satisfying u* = u, where * is the involution on FG defined by sending each element of G to its inverse. The conditions under which these symmetric units satisfy a group identity have now been determined. This book presents these results for arbitrary group identities, as well as the conditions under which the unit group or the set of symmetric units satisfies several particular group identities of interest.

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198

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Springer Science & Business Media

Published Date

ISBN 10

1849965048

ISBN 13

9781849965040

Group Representations

By: Gregory Karpilovsky

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Group Representations

By: Gregory Karpilovsky

This volume is divided into three parts. Part I provides the foundations of the theory of modular representations. Special attention is drawn to the Brauer-Swan theory and the theory of Brauer characters. A detailed investigation of quadratic, symplectic and symmetric modules is also provided. Part II is devoted entirely to the Green theory: vertices and sources, the Green correspondence, the Green ring, etc. In Part III, permutation modules are investigated with an emphasis on the study of p-permutation modules and Burnside rings. The material is developed with sufficient attention to detail so that it can easily be read by the novice, although its chief appeal will be to specialists. A number of the results presented in this volume have almost certainly never been published before.

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973

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Elsevier

Published Date

ISBN 10

1483295109

ISBN 13

9781483295107

Induced Modules over Group Algebras

By: G. Karpilovsky

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Induced Modules over Group Algebras

By: G. Karpilovsky

In 1898 Frobenius discovered a construction which, in present terminology, associates with every module of a subgroup the induced module of a group. This construction proved to be of fundamental importance and is one of the basic tools in the entire theory of group representations.This monograph is designed for research mathematicians and advanced graduate students and gives a picture of the general theory of induced modules as it exists at present. Much of the material has until now been available only in research articles. The approach is not intended to be encyclopedic, rather each topic is considered in sufficient depth that the reader may obtain a clear idea of the major results in the area.After establishing algebraic preliminaries, the general facts about induced modules are provided, as well as some of their formal properties, annihilators and applications. The remaining chapters include detailed information on the process of induction from normal subgroups, projective summands of induced modules, some basic results of the Green theory with refinements and extensions, simple induction and restriction pairs and permutation modules. The final chapter is based exclusively on the work of Weiss, presenting a number of applications to the isomorphism problem for group rings.

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Page Count

533

Publisher

Elsevier

Published Date

ISBN 10

0080872727

ISBN 13

9780080872728

Book's by Gregory Karpilovsky

Group Representations

Group Representations

Symmetric and G-algebras

Symmetric and G-algebras

Group Identities on Units and Symmetric Units of Group Rings

Group Identities on Units and Symmetric Units of Group Rings

Group Representations

Group Representations

Induced Modules over Group Algebras

Induced Modules over Group Algebras

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