Some Lie superalgebras associated

to the Weyl algebras

Author:
Ian M. Musson

Journal:
Proc. Amer. Math. Soc. **127** (1999), 2821-2827

MSC (1991):
Primary 17B35; Secondary 16W10

DOI:
https://doi.org/10.1090/S0002-9939-99-04976-X

Published electronically:
May 4, 1999

MathSciNet review:
1616633

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let be the Lie superalgebra . We show that there is a surjective homomorphism from to the Weyl algebra , and we use this to construct an analog of the Joseph ideal. We also obtain a decomposition of the adjoint representation of on and use this to show that if is made into a Lie superalgebra using its natural -grading, then . In addition, we show that if and are isomorphic as Lie superalgebras, then . This answers a question of S. Montgomery.

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Additional Information

**Ian M. Musson**

Affiliation:
Department of Mathematical Sciences, University of Wisconsin-Milwaukee, Milwaukee, Wisconsin 53201

Email:
musson@csd.uwm.edu

DOI:
https://doi.org/10.1090/S0002-9939-99-04976-X

Keywords:
Lie superalgebras,
Weyl algebras,
Joseph ideal

Received by editor(s):
February 7, 1997

Received by editor(s) in revised form:
December 9, 1997

Published electronically:
May 4, 1999

Additional Notes:
This research was partially supported by NSF grant DMS 9500486.

Communicated by:
Ken Goodearl

Article copyright:
© Copyright 1999
American Mathematical Society