Journal of Lie Theory EMIS ELibM Electronic Journals Journal of Lie Theory
Vol. 13, No. 2, pp. 427--442 (2003)

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On a Diffeological Group Realization of Certain Generalized Symmetrizable Kac-Moody Lie Algebras

Joshua Leslie

Joshua Leslie,
Mathematics Department,
Howard University
Washington, DC
USA
jleslie@howard.edu

Abstract: In this paper we utilize the notion of infinite dimensional diffeological Lie groups and diffeological Lie algebras to construct a Lie group structure on the space of smooth paths into a completion of a generalized Kac-Moody Lie algebra associated to a symmetrized generalized Cartan matrix. We then identify a large normal subgroup of this group of paths such that the quotient group has the sought-after properties of a candidate for a Lie group corresponding to the completion of the initial Kac Moody Lie algebra.

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Electronic version published on: 26 May 2003. This page was last modified: 14 Aug 2003.

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