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Varieties of topological groups generated by Lie groups

Published online by Cambridge University Press:  20 January 2009

Su-Shing Chen  and
Sidney A. Morris
Su-Shing Chen
Affiliation:
University of Florida, Gainesville, Florida, U.S.A.
Sidney A. Morris
Affiliation:
The University of New South Wales, Kensington, New South Wales, Australia
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Varieties of topological groups have been investigated in several papers ((2) and (10)-(13)). In this note we investigate the varieties generated by classical Lie groups. In particular we show results of which the following is indicative: The variety generated by the unitary group U(n) contains U(m) if and only if m ≦ n. En route we introduce the notion of a variety of topological Lie algebras which provides a convenient setting in which to answer our questions.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 18 , Issue 1 , June 1972 , pp. 49 - 53
Copyright
Copyright © Edinburgh Mathematical Society 1972

References

REFERENCES

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