Centers of universal enveloping algebras of Lie superalgebras in prime characteristic

2012/10/30 by Wei, Junyan, Zheng, Lisun, Shu, Bin
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1210.8032

Abstract

Let \ggg=\ggg_\bz+\ggg_\bo be a basic classical Lie superalgebra over an algebraically closed field k of characteristic p>2, and G be an algebraic supergroup satisfying \Lie(G)=\ggg, with the purely even subgroup G_\ev which is a reductive group. The center \cz:=\cz(\ggg) of the universal enveloping algebra of \ggg easily turns out to be a domain. In this paper, we prove that the quotient field of \cz coincides with that of the subalgebra generated by the G_\ev-invariant ring \cz^G_\ev of \cz and the p-center \cz₀ of U(\ggg_\bz).

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