K-regularity of locally convex algebras

TL;DR

This paper proves the K-regularity of certain locally convex algebras by establishing isomorphisms between various K-groups for monoid algebras over quasi-stable and quasi-stable Frechet algebras with bounded approximate units.

Contribution

It demonstrates the K-regularity property for quasi-stable Frechet algebras with bounded approximate units, linking Karoubi-Villamayor, Quillen, and smooth K-groups.

Findings

Karoubi-Villamayor K-groups are isomorphic to smooth K-groups for monoid algebras over quasi-stable locally convex algebras.

Quillen K-groups are isomorphic to smooth K-groups for monoid algebras over quasi-stable Frechet algebras with bounded approximate units.

K-regularity is established for these classes of algebras.

Abstract

The isomorphism of Karoubi-Villamayor K-groups with smooth K-groups for monoid algebras over quasi stable locally convex algebras is established and we prove that the Quillen K- groups are isomorphic to smooth K-groups for monoid algebras over quasi-stable Frechet algebras having a properly uniformly bounded approximate unit. Based on these results the K-regularity property for quasi-stable Frechet algebras having a properly uniformly bounded approximate unit is established.