An Integrability Condition for Simple Lie Groups II
Symmetry, integrability and geometry: methods and applications, Tome 11 (2015)
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It is shown that a simple Lie group $G$ ($ \neq {\rm SL}_2$) can be locally characterised by an integrability condition on an $\operatorname{Aut}(\mathfrak{g})$ structure on the tangent bundle, where $\operatorname{Aut}(\mathfrak{g})$ is the automorphism group of the Lie algebra of $G$. The integrability condition is the vanishing of a torsion tensor of type $(1,2)$. This is a slight improvement of an earlier result proved in [Min-Oo M., Ruh E. A., in Differential Geometry and Complex Analysis, Springer, Berlin, 1985, 205–211].
Keywords:
simple Lie groups and algebras; $G$-structure.
@article{SIGMA_2015_11_a26,
author = {Maung Min-Oo},
title = {An {Integrability} {Condition} for {Simple} {Lie} {Groups~II}},
journal = {Symmetry, integrability and geometry: methods and applications},
year = {2015},
volume = {11},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SIGMA_2015_11_a26/}
}
Maung Min-Oo. An Integrability Condition for Simple Lie Groups II. Symmetry, integrability and geometry: methods and applications, Tome 11 (2015). http://geodesic.mathdoc.fr/item/SIGMA_2015_11_a26/
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