Homological dimensions of analytic Ore extensions

Abstract

If $A$ is an algebra with finite right global dimension, then for any automorphism $\alpha$ and $\alpha$-derivation $\delta$ the right global dimension of $A[t;\alpha ,\delta ]$ satisfies \[ \text{rgld} \, A \le \text{rgld} \, A[t; α, δ] \le \text{rgld} \, A + 1. \] We extend this result to the case of holomorphic Ore extensions and smooth crossed products by $\mathbb{Z}$ of $\hat{\otimes }$-algebras.

arXiv comment20 pages, the paper was almost entirely rewritten since the inital upload