Isomorphisms of tensor algebras arising from weighted partial systems

TL;DR

This paper investigates the isomorphism classifications of tensor algebras derived from weighted partial dynamical systems, providing new criteria and alternative proofs for existing algebraic structures.

Contribution

It offers complete bounded and isometric classification results for tensor algebras from weighted partial systems, distinguishing between isometric and algebraic isomorphisms.

Findings

Complete classification results for tensor algebras from weighted partial systems.

Isometric and algebraic isomorphism problems are shown to be distinct.

Alternative proofs for existing classification results in related algebraic structures.

Abstract

We continue the study of isomorphisms of tensor algebras associated to a C*-correspondences in the sense of Muhly and Solel. Inspired by by recent work of Davidson, Ramsey and Shalit, we solve isomorphism problems for tensor algebras arising from weighted partial dynamical systems. We provide complete bounded / isometric classification results for tensor algebras arising from weighted partial systems, both in terms of the C*-correspondences associated to them, and in terms of the original dynamics. We use this to show that the isometric isomorphism and algebraic / bounded isomorphism problems are two distinct problems, that require separate criteria to be solved. Our methods yield alternative proofs to classification results for Peters' semi-crossed product due to Davidson and Katsoulis and for multiplicity-free graph tensor algebras due to Katsoulis, Kribs and Solel.