Homological dimensions of smooth crossed products

Abstract

In this paper we provide upper estimates for the global projective dimensions of smooth crossed products $\mathcal{S}(G,A;\alpha )$ for $G=\mathbb{R}$ and $G=\mathbb{T}$ and a self-induced Fréchet-Arens-Michael algebra $A$. In order to do this, we provide a powerful generalization of methods which are used in the works of Ogneva and Helemskii.

21 pages