Solution of a non-domestic tame classification problem from integral representation theory of finite groups ([Lambda]=RC,̂v(3)=4) / Ernst Dieterich.

Format:

Book

Author/Creator:

Dieterich, Ernst, 1951- author.

Series:

Memoirs of the American Mathematical Society ; Volume 92, Number 450.

Memoirs of the American Mathematical Society, 0065-9266 ; Volume 92, Number 450

Language:

English

Subjects (All):

Representations of groups.

Finite groups.

Modules (Algebra).

Physical Description:

1 online resource (165 p.)

Edition:

1st ed.

Place of Publication:

Providence, Rhode Island : American Mathematical Society, 1991.

Language Note:

English

Summary:

Suppose R is a complete discrete valuation ring with exponential valuation v, G is a finite p-group. The representation type (finite, tame, or wild) of the group ring *L = RG had been determined in all cases but one; the case in which G = C3 and v(3)=4. The present book closes this gap. The author presents an explicit classification of all indecomposable lattices, as well as a description of the Auslander-Reiten quiver of *L, demonstrating that this is the only integral group ring whose representation type is non-domestic tame of finite growth. This book acquaints readers with various (by now classical) tame module categories, with techniques of matrix reduction, and with the interaction of basefree (category-theoretic) and base-dependent (matrix-theoretic) viewpoints and their respective relations to the combinatorial intuition provided by Auslander-Reiten quivers.

Contents:

Intro

TABLE OF CONTENTS

INTRODUCTION

0. PRELIMINARIES

0.1. Notation and Conventions

0.2. Generalized factorspace categories

0.3. Normal forms for local problems

0.4. Angular matrices and definition of subcategories

0.5. Dimension mappings

1. FIRST REDUCTION

2. SECOND REDUCTION

3. THIRD REDUCTION

4. FOURTH REDUCTION

5. THE AUSLANDER REITEN QUIVER OF Λ

6. APPENDIX

6.1. Complete list of all indecomposable Λ lattices

6.2. The Auslander-Reiten quiver of M

6.3. Leitfaden

REFERENCES.

Notes:

"July 1991, Volume 92, Number 450 (third of 4 numbers)."

Includes bibliographical references.

Description based on print version record.

ISBN:

1-4704-0876-7