Noncommutative localizations of a contractive quantum plane

Abstract

In the present paper we investigate the localizations in the sense of J. L. Taylor of the Arens-Michael-Fr\'echet algebras associated with noncommutative analytic spaces of a contractive q-plane representing its formal geometry. It turns out that all noncommutative Fr\'echet algebras obtained by the Fr\'echet algebra structure sheaves over open subsets from the topology bases are indeed localizations. That topological homology property of the structure sheaves results in the key properties of Taylor and Putinar spectra of the left Banach q-modules over the algebras of global sections.