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Galois Algebras and Monoidal Functors between Categories of Representations of Finite Groups

✍ Scribed by A.A Davydov

Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
194 KB
Volume
244
Category
Article
ISSN
0021-8693

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✦ Synopsis

We use relations between Galois algebras and monoidal functors to describe monoidal functors between categories of representations of finite groups. We pay special attention to two kinds of these monoidal functors: monoidal functors to vector spaces and monoidal equivalences between categories of representations. The functors of the second kind induce isomorphisms of character tables. We show that pairs of groups with the same character table obtained in this way are a generalization of the construction proposed by B. Fischer (1988, Rend. Circ. Mat. Palermo (2) Suppl. 19, 71-77).  2001 Academic Press CONTENTS 1. Introduction. 2. Galois algebras and monoidal functors. 3. Description of group Galois algebras. 4. Special automorphisms of twisted group algebras. 5. Automorphisms of Galois algebras. 6. Bi-Galois algebras and monoidal equivalences. 7. Cohomology calculations. 8. Characters of Galois algebras.

  1. INTRODUCTION It is well known [11, 10] that monoidal functors from the category of representations of a Hopf algebra gives rise to certain Galois-type algebraic 273

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