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Finite groups with the same character tables, Drinfel'd algebras and Galois algebras

A. Davydov
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Abstract

We prove that finite groups have the same complex character tables iff the group algebras are twisted forms of each other as Drinfel'd quasi-bialgebras or iff there is non-associative bi-Galois algebra over these groups. The interpretations of class-preserving automorphisms and permutation representations with the same character in terms of Drinfel'd algebras are also given.

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A. Davydov. 2000-01-22. Finite groups with the same character tables, Drinfel'd algebras and Galois algebras. https://arxiv.org/abs/math/0001119

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