Abstract
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.
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Ginosar, Y., Schnabel, O. Semi-invariant Matrices over Finite Groups. Algebr Represent Theor 17, 199–212 (2014). https://doi.org/10.1007/s10468-012-9394-7
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DOI: https://doi.org/10.1007/s10468-012-9394-7