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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
DOI: https://doi.org/10.1090/S0002-9947-1974-0352334-6
MathSciNet review: 0352334
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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.


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