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Journal of the London Mathematical Society 1996 53(1):39-49; doi:10.1112/jlms/53.1.39
© 1996 by London Mathematical Society
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© The London Mathematical Society

A Bijection of Primitive Spectra for Classical Lie Superalgebras of Type I

Edward S. Letzter

Department of Mathematics, Texas A & M University College Station, Texas 77840, USA E-mail: letzter{at}math.tamu.edu

Received 22 November 1993. Revision received 18 May 1994.

A description of the set of primitive ideals is obtained for the enveloping algebra V of a classical Lie superalgebra g = g0 {oplus} g1 in the series A(m, n), C(n), P(n). In particular, a bijective function is presented from prim V onto the well-known set prim U, where U denotes the enveloping algebra of the reductive Lie algebra g0. This function, dependent only upon a choice of adg0-composition series for g1, extends in part a correspondence established by V. G. Kac between equivalence classes of finite dimensional irreducible representations. Our methods rely on I. M. Musson's extension of Duflo's Theorem to classical Lie superalgebras and on our previous studies of noetherian ring extensions. While the above function extends to a bijection between prime spectra, it does not preserve inclusions and so does not reveal the topological structure.

This research was completed while the author held an NSF postdoctoral research fellowship at the University of Utah.


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