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

Abstract

If g is a classical simple Lie superalgebra (g≠P(n)), the enveloping algebra U(g) is a prime ring and hence has a simple artinian ring of quotients Q(U(g)) by Goldie's Theorem. We show that if g has Type I then Q(U(g)) is a matrix ring over Q(U(g0)). On the other hand, if g=osp(1,2r) then by extending the center of U(g) 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.