Geodesic
On a Diffeological Group Realization of Certain Generalized Symmetrizable Kac-Moody Lie Algebras
Journal of Lie theory, Tome 13 (2003) no. 2, pp. 427-442
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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. 
@article{JLT_2003_13_2_JLT_2003_13_2_a6,
     author = {J. Leslie},
     title = {On a {Diffeological} {Group} {Realization} of {Certain} {Generalized} {Symmetrizable} {Kac-Moody} {Lie} {Algebras}},
     journal = {Journal of Lie theory},
     pages = {427--442},
     year = {2003},
     volume = {13},
     number = {2},
     url = {http://geodesic.mathdoc.fr/item/JLT_2003_13_2_JLT_2003_13_2_a6/}
}
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J. Leslie. On a Diffeological Group Realization of Certain Generalized Symmetrizable Kac-Moody Lie Algebras. Journal of Lie theory, Tome 13 (2003) no. 2, pp. 427-442. http://geodesic.mathdoc.fr/item/JLT_2003_13_2_JLT_2003_13_2_a6/