An Integrability Condition for Simple Lie Groups II

Symmetry Integrability and Geometry-Methods and Applications

article

Maung Min-Oo¹ 

[1] Department of Mathematics & Statistics, McMaster University

关键词: simple Lie groups and algebras;    G-structure;   

DOI  :  10.3842/SIGMA.2015.027

来源: National Academy of Science of Ukraine

【 摘 要 】

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].

【 授权许可】

Unknown