A BIJECTION OF PRIMITIVE SPECTRA FOR CLASSICAL LIE-SUPERALGEBRAS OF TYPE-I

A description of the set of primitive ideals is obtained for the envel oping algebra V of a classical Lie superalgebra g = g(0) circle plus g (1) in the series A(m,n), C(n), P(n). In particular, a bijective funct ion is presented from prim V onto the well-known set prim U, where U d enotes the enveloping algebra of the reductive Lie algebra g(0). This function, dependent only upon a choice of adg(0)-composition series fo r g(1), extends in part a correspondence established by V. G. Kac betw een equivalence classes of finite dimensional irreducible representati ons. Our methods rely on I. M. Musson's extension of Duflo's Theorem t o classical Lie superalgebras and on our previous studies of noetheria n ring extensions. While the above function extends to a bijection bet ween prime spectra, it does not preserve inclusions and so does not re veal the topological structure.