On the Goldie Quotient Ring of the Enveloping Algebra of a Classical Simple Lie Superalgebra,

If is a classical simple Lie superalgebra ( ≠ P(n)), the enveloping algebra U( ) is a prime ring and hence has a simple artinian ring of quotients Q(U( )) by Goldieʹs Theorem. We show that if has Type I then Q(U( )) is a matrix ring over Q(U( 0)). On the other hand, if = osp(1, 2r) then by extending the center of U( ) we obtain a prime ring whose Goldie quotient ring is a matrix ring over the quotient division ring of a Weyl algebra. This is an analog of a result of Gelfand and Kirillov.