Journal of Lie Theory 23 (2013), No. 3, 731--745
Copyright Heldermann Verlag 2013
Left Invariant Metrics on Lie Groups Associated with G-Associative Algebras
Chengming Bai
Chern Institute of Mathematics and LPMC, Nankai University, Tianjin 300071, P. R. China
baicm@nankai.edu.cn
Zhiqi Chen
School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, P. R. China
chenzhiqi@nankai.edu.cn
A left invariant connection associated with a left invariant metric on a Lie group defines a Lie-admissible algebra which provides a Lie-admissible algebraic approach to the study given by Milnor. In this paper, using such an approach, we study left invariant metrics on Lie groups associated with certain subclasses of Lie-admissible Lie algebras, namely, G-associative algebras explicitly. In particular, their classifications in low dimensions are given.
Keywords: Left invariant metric, Lie group, Lie algebra, Lie-admissible algebra, G-associative algebra.
MSC: 17D25, 17A30, 53C07
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