Minimal prime ideals in enveloping algebras of Lie superalgebras

Kirkman, Ellen; Kuzmanovich, James

doi:10.1090/S0002-9939-96-03230-3

Minimal prime ideals in enveloping algebras of Lie superalgebras
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by Ellen Kirkman and James Kuzmanovich PDF

Proc. Amer. Math. Soc. 124 (1996), 1693-1702 Request permission

Abstract:

Let ${\frak g}$ be a finite dimensional Lie superalgebra over a field of characteristic zero. Let $U({\frak g})$ be the enveloping algebra of ${\frak g}$. We show that when ${\frak g} = b(n)$, then $U({\frak g})$ is not semiprime, but it has a unique minimal prime ideal; it follows then that when ${\frak g}$ is classically simple, $U({\frak g})$ has a unique minimal prime ideal. We further show that when ${\frak g}$ is a finite dimensional nilpotent Lie superalgebra, then $U({\frak g})$ has a unique minimal prime ideal.

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