Geodesic
Left Invariant Metrics on Lie Groups Associated with G-Associative Algebras
Journal of Lie theory, Tome 23 (2013) no. 3, pp. 731-745
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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.
Classification : 17D25, 17A30, 53C07
Mots-clés : Left invariant metric, Lie group, Lie algebra, Lie-admissible algebra, G-associative algebra 
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     author = {C. Bai and Z. Chen},
     title = {Left {Invariant} {Metrics} on {Lie} {Groups} {Associated} with {G-Associative} {Algebras}},
     journal = {Journal of Lie theory},
     pages = {731--745},
     year = {2013},
     volume = {23},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JLT_2013_23_3_JLT_2013_23_3_a7/}
}
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C. Bai; Z. Chen. Left Invariant Metrics on Lie Groups Associated with G-Associative Algebras. Journal of Lie theory, Tome 23 (2013) no. 3, pp. 731-745. http://geodesic.mathdoc.fr/item/JLT_2013_23_3_JLT_2013_23_3_a7/