ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

2. Algebra

1991 MS Classification: 20C05 Davydov, A. A., Moscow State University, Russia Drinfel’d theory and representations of finite groups The theory of quasi-Hopf algebras was developed by V. G. Drinfeld́ for the describtion of quantization of Lie groups. This theory seems to be very suitible for reformulating of various problems of representation theory of finite groups. The key observations is that any map of character tables of finite groups corresponds to the quasi-homomorphism of the group algebras considered as quasi-Hopf algebras and any two quasi-homomorphisms of the group algebras define the same map of character tables iff they are twisted forms. In particular, we can give the definitions in terms of (quasi-)Hopf algebras of such objects as class-preserving automorphisms, permutation representations with the same character, groups with the same character table.