Minimal prime ideals in enveloping algebras of Lie superalgebras
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- by Ellen Kirkman and James Kuzmanovich
- Proc. Amer. Math. Soc. 124 (1996), 1693-1702
- DOI: https://doi.org/10.1090/S0002-9939-96-03230-3
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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.References
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Bibliographic Information
- Ellen Kirkman
- Affiliation: Department of Mathematics Wake Forest University Winston-Salem, North Carolina 27109
- MR Author ID: 101920
- Email: kirkman@mthcsc.wfu.edu
- James Kuzmanovich
- Affiliation: Department of Mathematics Wake Forest University Winston-Salem, North Carolina 27109
- Email: kuz@mthcsc.wfu.edu
- Received by editor(s): August 12, 1994
- Received by editor(s) in revised form: December 13, 1994
- Additional Notes: The first author was supported in part by a grant from the National Security Agency.
- Communicated by: Ken Goodearl
- © Copyright 1996 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 124 (1996), 1693-1702
- MSC (1991): Primary 16S30; Secondary 16D30, 17B35, 17A70
- DOI: https://doi.org/10.1090/S0002-9939-96-03230-3
- MathSciNet review: 1307538