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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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] Nathan Jacobson, Lie algebras, Interscience Tracts in Pure and Applied Mathematics, No. 10, Interscience Publishers (a division of John Wiley & Sons), New York-London, 1962. MR 0143793
  • [2] John Milnor, Curvatures of left invariant metrics on Lie groups, Advances in Math. 21 (1976), no. 3, 293–329. MR 0425012

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1087471-0
Keywords: $ 3$-dimensional Lie algebra
Article copyright: © Copyright 1992 American Mathematical Society