Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



The category of generalized Lie groups

Authors: Su Shing Chen and Richard W. Yoh
Journal: Trans. Amer. Math. Soc. 199 (1974), 281-294
MSC: Primary 22E65
MathSciNet review: 0352334
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We consider the category $\Gamma$ of generalized Lie groups. A generalized Lie group is a topological group $G$ such that the set $LG = Hom({\mathbf {R}},G)$ of continuous homomorphisms from the reals ${\mathbf {R}}$ into $G$ has certain Lie algebra and locally convex topological vector space structures. The full subcategory ${\Gamma ^r}$ of $r$-bounded ($r$ positive real number) generalized Lie groups is shown to be left complete. The class of locally compact groups is contained in $\Gamma$. Various properties of generalized Lie groups $G$ and their locally convex topological Lie algebras $LG = Hom({\mathbf {R}},G)$ are investigated.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 22E65

Retrieve articles in all journals with MSC: 22E65

Additional Information

Keywords: Generalized Lie group, Lie group, Lie algebra, locally convex topological Lie algebra, category, left completeness
Article copyright: © Copyright 1974 American Mathematical Society