1Dept. of Mathematics, Howard University, Washington, DC, U.S.A. 2We 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. 3[
Journal of Lie Theory, Tome 13 (2003) no. 2, pp. 427-442
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Joshua 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/JOLT_2003_13_2_a6/
@article{JOLT_2003_13_2_a6,
author = {Joshua 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/JOLT_2003_13_2_a6/}
}
TY - JOUR
AU - Joshua Leslie
TI - On a Diffeological Group Realization of Certain Generalized Symmetrizable Kac-Moody Lie Algebras
JO - Journal of Lie Theory
PY - 2003
SP - 427
EP - 442
VL - 13
IS - 2
UR - http://geodesic.mathdoc.fr/item/JOLT_2003_13_2_a6/
ID - JOLT_2003_13_2_a6
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%0 Journal Article
%A Joshua Leslie
%T On a Diffeological Group Realization of Certain Generalized Symmetrizable Kac-Moody Lie Algebras
%J Journal of Lie Theory
%D 2003
%P 427-442
%V 13
%N 2
%U http://geodesic.mathdoc.fr/item/JOLT_2003_13_2_a6/
%F JOLT_2003_13_2_a6
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.
