The semi-center of an artinian semisimple module-algebra over a finite group G can be described using the projective representations of G. In particular, the semi-center of the endomorphism ring of an irreducible projective representation over an algebraically closed field has a structure of a twisted group algebra. The following group-theoretic result is deduced: the center of a group of central type embeds into the group of its linear characters.
- Projective representation
- Twisted group algebra
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