

Globus Seminar
October 6, 2011 15:40, Moscow, IUM (Bolshoi Vlas'evskii per., 11)






A quantum generalization of the schur multiplier
Ch. Kassel^{ab} ^{a} Centre National de la Recherche Scientifique, Paris
^{b} Strasbourg University

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Abstract:
One hundred years ago Schur defined the socalled multiplier of a group $G$ in order to classify the projective representations of $G$. Around 1990 Drinfeld introduced what are now called Drinfeld twists in order to classify quantum groups. Invariant Drinfeld twists form a group which can be defined for any Hopf algebra. I'll point out that this group for some Hopf algebra coincides with the Schur multiplier of a finite group. I'll show how to compute this group of invariant Drinfeld twists for the group algebra of a finite group $G$. The answer involves a Galois cohomology group, the group of automorphisms of $G$ preserving conjugacy classes, and the normal abelian subgroups of $G$ of central type. I'll illustrate this with several examples of wellknown finite groups. My talk is based on joint work with Pierre Guillot published in [1].
Language: English
References

P. Guillot, Ch. Kassel, “Cohomology of invariant Drinfeld twists on group algebras”, Int. Math. Res. Not., 2010:10 (2010), 1894–1939, arXiv: 0903.2807

