An invariant on 3-dimensional Lie algebras

Tasaki, Hiroyuki; Umehara, Masaaki

doi:10.1090/S0002-9939-1992-1087471-0

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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An invariant on $3$-dimensional Lie algebras
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by Hiroyuki Tasaki and Masaaki Umehara PDF

Proc. Amer. Math. Soc. 115 (1992), 293-294 Request permission

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

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John Milnor, Curvatures of left invariant metrics on Lie groups, Advances in Math. 21 (1976), no. 3, 293–329. MR 425012, DOI 10.1016/S0001-8708(76)80002-3