
Journal of Lie Theory 23 (2013), No. 3, 731745 Copyright Heldermann Verlag 2013 Left Invariant Metrics on Lie Groups Associated with GAssociative 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 Lieadmissible algebra which provides a Lieadmissible 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 Lieadmissible Lie algebras, namely, Gassociative algebras explicitly. In particular, their classifications in low dimensions are given. Keywords: Left invariant metric, Lie group, Lie algebra, Lieadmissible algebra, Gassociative algebra. MSC: 17D25, 17A30, 53C07 [ Fulltextpdf (286 KB)] for subscribers only. 