A criterion for primeness of enveloping algebras of Lie superalgebras

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Abstract (in LaTeX)

We show that if the determinant of a certain matrix obtained from
the Lie product on the odd part of a Lie superalgebra is nonzero,
then the enveloping algebra of the Lie superalgebra is a prime
ring.  We then apply this criterion to show that the enveloping
algebra of a classical simple Lie superalgebra not of type $b(n)$
is a prime ring.

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