Block representation type of reduced enveloping algebras

Gordon, Iain; Premet, Alexander

doi:10.1090/S0002-9947-01-02826-4

Block representation type of reduced enveloping algebras
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by Iain Gordon and Alexander Premet

Trans. Amer. Math. Soc. 354 (2002), 1549-1581

DOI: https://doi.org/10.1090/S0002-9947-01-02826-4

Published electronically: December 7, 2001

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Abstract:

Let $K$ be an algebraically closed field of characteristic $p$, $G$ a connected, reductive $K$-group, $\mathfrak {g}=\text {Lie}(G)$, $\chi \in \mathfrak {g}^*$ and $U_\chi (\mathfrak {g})$ the reduced enveloping algebra of $\mathfrak {g}$ associated with $\chi$. Assume that $G^{(1)}$ is simply-connected, $p$ is good for $G$ and $\mathfrak {g}$ has a non-degenerate $G$-invariant bilinear form. All blocks of $U_\chi (\mathfrak {g})$ having finite and tame representation type are determined.

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