A.D. Bell: Abstract

## Primitive factors of enveloping algebras of nilpotent Lie superalgebras

### Author(s)

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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