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

Joshua Leslie

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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