ON THE HARISH-CHANDRA HOMOMORPHISM FOR GENERALIZED KAC-MOODY ALGEBRAS

Abstract

We attempt to refine Kac's arguments and to generalize them to the case of generalized Kac-Moody algebras in order to study an isomorphism between the center of (a completion of) the universal enveloping algebra and the algebra of complex-valued functions on the dual of the Cartan subalgebra with certain infinitely many affine hyperplanes removed.

Keywords:

• Generalized Kac-Moody algebras
• Harish-Chandra homomorphism
• 1991 Mathematics Subject Classification Primary 17B67; 17B65; 17B70; Secondary 17B55

ACKNOWLEDGMENTS

I would like to express my sincere thanks to V. G. Kac for discussions and for giving me an offprint of his paper [3].