A.D. Bell: Abstract

Primitive factors of enveloping algebras of nilpotent Lie superalgebras


Allen D. Bell and Ian M. Musson

Publication Information

Appeared in Journal of the London Mathematical Society (2) 42 (1990), pp. 401-408
Math Reviews: 92b:17013

Abstract (in LaTex)

We show that if $U$ is the enveloping algebra of a finite-dimensional
nilpotent Lie superalgebra over a field of characteristic zero, then
any graded-primitive factor ring of $U$ is isomorphic to a tensor
product $C\otimes_k A$ where $C$ is the Clifford algebra of a
nonsingular form over some finite field extension of $k$ and $A$ is
a Weyl algebra over $k$.  We prove that the same result holds for
a primitive factor of $U$, except that $C$ may be either the whole
Clifford algebra or just its even part.  We give examples to show
all possibilities can occur.  Our results generalize a result of
Dixmier for ordinary Lie algebras.

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