Endomorphism rings of simple modules over group rings

Snider, Robert

doi:10.1090/S0002-9939-96-03368-0

Endomorphism rings of simple modules over group rings
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by Robert L. Snider

Proc. Amer. Math. Soc. 124 (1996), 1043-1049

DOI: https://doi.org/10.1090/S0002-9939-96-03368-0

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Abstract:

If $N$ is a finitely generated nilpotent group which is not abelian-by-finite, $k$ a field, and $D$ a finite dimensional separable division algebra over $k$, then there exists a simple module $M$ for the group ring $k[G]$ with endomorphism ring $D$. An example is given to show that this cannot be extended to polycyclic groups.

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