K-regularity of locally convex algebras

The isomorphism of Karoubi–Villamayor K -groups with smooth K -groups for monoid algebras over quasi-stable locally convex algebras is established. We prove that the Quillen K -groups are isomorphic to smooth K -groups for monoid algebras over quasi-stable Fr e ´ chet algebras having a properly unif...

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Bibliographic Details
Published in:Journal of homotopy and related structures 2016-12, Vol.11 (4), p.869-884
Main Author: Inassaridze, Hvedri
Format: Article
Language:English
Subjects:
Algebra
Algebraic Topology
Functional Analysis
Group theory
Isomorphism
Mathematics
Mathematics and Statistics
Number Theory
Regularity
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Summary:The isomorphism of Karoubi–Villamayor K -groups with smooth K -groups for monoid algebras over quasi-stable locally convex algebras is established. We prove that the Quillen K -groups are isomorphic to smooth K -groups for monoid algebras over quasi-stable Fr e ´ chet algebras having a properly uniformly bounded approximate unit and not necessarily m -convex. Based on these results the K -regularity property for quasi-stable Fr e ´ chet algebras having a properly uniformly bounded approximate unit is established.
ISSN:2193-8407
1512-2891
DOI:10.1007/s40062-016-0155-x