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XI.—On the Construction of Metrisable Lie Algebras*

Published online by Cambridge University Press:  14 February 2012

S-T. Tsou
S-T. Tsou
Affiliation:
Department of Mathematics, University of Hong Kong.
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Extract

The concept of metrisable Lie algebras was introduced in a previous paper, where some fundamental properties of metrisable Lie algebras have been given. It was shown that, associated with an admissible metric tensor of a metrisable Lie algebra, there is a unique antisymmetric tensor of the third order. A complete solution of the converse problem will be given in this paper; it is first reducedto the solution of a system of algebraic equations and then it is proved that, there always exists a unique metrisable Lie algebra corresponding to each symmetricsolution of the system, even when the solution is trivial. The Lie algebra thus obtained is a reduced metrisable Lie algebra.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 66 , Issue 2 , 1962 , pp. 116 - 127
Copyright
Copyright © Royal Society of Edinburgh 1962

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References

page 116 note † , S- T. Tsou and Walker, A. G., Proc. Roy. Soc. Edin., A, 64, 1957, 290–304.Google Scholar

page 116 note ‡ , Tsou and , Walker, loc. cit., p. 296.Google Scholar

page 121 note * Tsou and Walker, loc. cit., p. 296.

page 124 note * Tsou and Walker, loc. cit., p. 298.

page 124 note † See Appendix.

page 126 note * Tsou and Walker, loc. cit., [6.1], p. 297.