Generalized reductive algebras and a quantum example

Daniel R. Farkas, Gail Letzter and Lance W. Small

Vol. 221 (2005), No. 1, 29–48

DOI: 10.2140/pjm.2005.221.29

Abstract

The universal enveloping algebra of a semisimple Lie algebra is FCR. Complete reducibility for finite-dimensional modules is generalized to encompass the representations of reductive Lie algebras. A quantum example is presented as a nontrivial illustration of these ideas.

Keywords

reductive algebras, quantum symmetric pairs, residually finite-dimensional

Mathematical Subject Classification 2000

Primary: 17B37, 16H05

Milestones

Received: 25 March 2003

Revised: 25 November 2003

Accepted: 23 June 2004

Published: 1 September 2005