局部凸代数的k -正则性

IF 0.5 4区数学

Journal of Homotopy and Related Structures Pub Date : 2016-10-19 DOI:10.1007/s40062-016-0155-x

Hvedri Inassaridze

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引用次数: 0

摘要

建立了拟稳定局部凸代数上单代数的Karoubi-Villamayor k群与光滑k群的同构性。证明了拟稳定Fr \(\acute{\mathrm{e}}\)上具有适当一致有界近似单位且不一定是m凸的单群代数的Quillen k群与光滑k群是同构的。在此基础上，建立了具有适当一致有界近似单位的拟稳定Fr \(\acute{\mathrm{e}}\)代数的k -正则性。

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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\(\acute{\mathrm{e}}\)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\(\acute{\mathrm{e}}\)chet algebras having a properly uniformly bounded approximate unit is established.

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来源期刊

Journal of Homotopy and Related Structures Mathematics-Geometry and Topology

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期刊介绍： Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences. Journal of Homotopy and Related Structures is intended to publish papers on Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.