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Centers and Azumaya loci of finite -algebras
In this paper, we study the center of the finite -algebra
associated with a semi-simple Lie algebra
over an algebraically closed field \mathds{k} of
characteristic , and an arbitrarily given nilpotent element
. We obtain an analogue of Veldkamp's theorem on the center.
For the maximal spectrum , we show that its Azumaya locus
coincides with its smooth locus of smooth points. The former locus reflects
irreducible representations of maximal dimension for
.Comment: 31 page
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