Enveloping algebras of Lie groups with discrete series

Nguyen Huu Anh and Vuong Manh Son

Vol. 156 (1992), No. 1, 1–18

DOI: 10.2140/pjm.1992.156.1

Abstract

In this article we shall prove that the enveloping algebra of the Lie algebra of a class of unimodular Lie groups having discrete series, when localized at some element of the center, is isomorphic to the tensor product of a Weyl algebra over the ring of Laurent polynomials of one variable and the enveloping algebra of some reductive algebra. In particular, it will be proved that the Lie algebra of a unimodular solvable Lie group having discrete series satisfies the Gelfand-Kirillov conjecture.

Mathematical Subject Classification 2000

Primary: 17B35

Secondary: 22E47

Milestones

Received: 3 December 1990

Revised: 22 October 1991

Published: 1 November 1992