Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
MathSciNet review: 1307538
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 16S30, 16D30, 17B35, 17A70

Retrieve articles in all journals with MSC (1991): 16S30, 16D30, 17B35, 17A70


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: http://dx.doi.org/10.1090/S0002-9939-96-03230-3
PII: S 0002-9939(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