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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

Zhiqi Chen
School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, P. R. China

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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