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Proceedings of the American Mathematical Society

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An invariant on $ 3$-dimensional Lie algebras

Authors: Hiroyuki Tasaki and Masaaki Umehara
Journal: Proc. Amer. Math. Soc. 115 (1992), 293-294
MSC: Primary 17B05
MathSciNet review: 1087471
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Abstract: We construct an extra symmetric bilinear form on a $ 3$-dimensional Lie algebra $ \mathfrak{g}$ which induces an invariant $ \chi \left( \mathfrak{g} \right)$ on $ \mathfrak{g}$. Moreover it provides a new viewpoint for the classical classification of $ 3$-dimensional Lie algebras

References [Enhancements On Off] (What's this?)

  • [1] N. Jacobson, Lie algebras, Intersci. Tracts in Pure Appl. Math., vol. 10, John Wiley-Sons, New York, 1962. MR 0143793 (26:1345)
  • [2] J. Milnor, Curvature of left invariant metrics on Lie groups, Adv. in Math. 21 (1976), 293-329. MR 0425012 (54:12970)

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Keywords: $ 3$-dimensional Lie algebra
Article copyright: © Copyright 1992 American Mathematical Society

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