Minimal prime ideals in enveloping algebras of Lie superalgebras

Authors:
Ellen Kirkman and James Kuzmanovich

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

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a finite dimensional Lie superalgebra over a field of characteristic zero. Let be the enveloping algebra of . We show that when , then is not semiprime, but it has a unique minimal prime ideal; it follows then that when is classically simple, has a unique minimal prime ideal. We further show that when is a finite dimensional nilpotent Lie superalgebra, then has a unique minimal prime ideal.

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Additional Information

**Ellen Kirkman**

Affiliation:
Department of Mathematics Wake Forest University Winston-Salem, North Carolina 27109

Email:
kirkman@mthcsc.wfu.edu

**James Kuzmanovich**

Affiliation:
Department of Mathematics Wake Forest University Winston-Salem, North Carolina 27109

Email:
kuz@mthcsc.wfu.edu

DOI:
https://doi.org/10.1090/S0002-9939-96-03230-3

Keywords:
Enveloping algebra,
Lie superalgebra,
minimal prime ideals

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

Article copyright:
© Copyright 1996
American Mathematical Society