Varieties of topological groups generated by Lie groups
- 1 June 1972
- journal article
- research article
- Published by Cambridge University Press (CUP) in Proceedings of the Edinburgh Mathematical Society
- Vol. 18 (1) , 49-53
- https://doi.org/10.1017/s0013091500026146
Abstract
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.Keywords
This publication has 7 references indexed in Scilit:
- Generating varieties of topological groupsProceedings of the Edinburgh Mathematical Society, 1973
- Varieties of locally convex topological vector spacesBulletin of the American Mathematical Society, 1971
- Varieties of topological groups IIIBulletin of the Australian Mathematical Society, 1970
- Varieties of topological groups IIBulletin of the Australian Mathematical Society, 1970
- Varieties of topological groupsBulletin of the Australian Mathematical Society, 1969
- Varieties of GroupsPublished by Springer Nature ,1967
- On the existence of free subgroups in topological groupsFundamenta Mathematicae, 1957