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The dimension subalgebra problem for enveloping algebras of Lie superalgebras

Author: David M. Riley
Journal: Proc. Amer. Math. Soc. 123 (1995), 2975-2980
MSC: Primary 17B35; Secondary 16S30
MathSciNet review: 1264829
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Abstract: Let L be an arbitrary Lie superalgebra over a field of characteristic different from 2. Denote by $ \omega u(L)$ the ideal generated by L in its universal enveloping algebra $ U(L)$. It is shown that $ L \cap \omega u{(L)^n} = {\gamma _n}(L)$ for each $ n \geq 1$, where $ {\gamma _n}(L)$ is the nth term of the lower central series of L. We also prove that $ \omega u(L)$ is a residually nilpotent ideal if and only if L is residually nilpotent. Both these results remain true in characteristic 2 provided we take L to be an ordinary Lie algebra.

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