Piecewise conjugacy for multivariable dynamics over the Jacobson spectrum of a C*-algebra

TL;DR

This paper proves that automorphic multivariable C*-dynamical systems with isometrically isomorphic tensor algebras are piecewise conjugate over their Jacobson spectrum, resolving a previously posed question.

Contribution

It establishes a connection between algebraic isomorphisms and piecewise conjugacy in multivariable C*-dynamical systems over the Jacobson spectrum.

Findings

Isometric isomorphism of tensor algebras implies piecewise conjugacy

Addresses a question posed by Kakariadis and the author

Advances understanding of multivariable C*-dynamics

Abstract

We show that if (A,a) and (B,b) are automorphic multivariable C*-dynamical systems with isometrically isomorphic tensor algebras (or semi crossed products), then the systems are piecewise conjugate over their Jacobson spectrum. This answers a question of Kakariadis and the author.