Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-27T10:55:04.763Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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.