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On a diffeological group realization of certain generalized symmetrizable Kac-Moody Lie algebras. (English) Zbl 1119.17303

Summary: 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.

MSC:

17B67 Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras
22E20 General properties and structure of other Lie groups
22E65 Infinite-dimensional Lie groups and their Lie algebras: general properties
58B25 Group structures and generalizations on infinite-dimensional manifolds
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