Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1893689 | Journal of Geometry and Physics | 2012 | 11 Pages |
Abstract
Left invariant flat metrics on Lie groups are revisited in terms of left-symmetric algebras which correspond to affine structures. There is a left-symmetric algebraic approach with an explicit formula to the classification theorem given by Milnor. When the positive definiteness of the metric is replaced by nondegeneracy, there are many more examples of left invariant flat pseudo-metrics, which play important roles in several fields in geometry and mathematical physics. We give certain explicit constructions of these structures. Their classification in low dimensions and some interesting examples in higher dimensions are also given.
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Physical Sciences and Engineering
Mathematics
Mathematical Physics
Authors
Zhiqi Chen, Dongping Hou, Chengming Bai,