Module Categories of Analytic Groups

Andy R. Magid

doi:10.1017/CBO9780511897177

Knowledge of an analytic group implies knowledge of its module category. However complete knowledge of the category does not determine the group. Professor Magid shows here that the category determines another, larger group and an algebra of functions in this new group. The new group and its function algebra are completely described; this description thus tells everything that is known when the module category, as a category, is given. This categorical view brings together and highlights the significance of earlier work in this area by several authors, as well as yielding new results. By including many examples and computations Professor Magid has written a complete account of the subject that is accessible to a wide audience. Graduate students and professionals who have some knowledge of algebraic groups, Lie groups and Lie algebras will find this a useful and interesting text.

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Module Categories of Analytic Groups

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Contents

Frontmatter
pp i-iv

Contents
pp v-vi

Preface
pp vii-viii

Notation and conventions
pp ix-x

Introduction
pp 1-14

1 - Definitions and examples
pp 15-31

2 - Representative functions
pp 32-57

3 - Analytic subgroups of algebraic groups
pp 58-80

4 - Structure theory of algebras of representative functions
pp 81-103

5 - Left algebraic groups
pp 104-126

Appendix: Commutative analytic groups and characters
pp 127-130

Notes
pp 131-132

Bibliography
pp 133-133

Index
pp 134-134

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