An obstruction to isomorphism of tensor algebras of multivariable dynamical systems

2025/05/05 by Boris Bilich, Bilich, Boris · 1 citation
Computer Science · Mathematics · #37B20 #46H20 #46L55 #47L30 #Advanced Differential Equations and Dynamical Systems #FOS: Mathematics #Operator Algebras (math.OA) #Polynomial and algebraic computation #Tensor decomposition and applications

paper · pdf · doi:10.48550/arxiv.2505.02960

openalex publication_date 2025/05/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In their paper on multivariable dynamics, Davidson and Katsoulis conjectured that two multivariable dynamical systems have isomorphic tensor algebras if and only if they are piecewise conjugate. We disprove the conjecture by constructing two piecewise conjugate multivariable dynamical systems with four maps on a two-dimensional space, whose tensor algebras are not isomorphic.

Cited by

• Twisted topological correspondences and Cartan subalgebras

Related

• The isomorphism problem for tensor algebras of multivariable dynamical systems
• Piecewise conjugacy for multivariable dynamics over the Jacobson spectrum of a C*-algebra
• Operator algebras for multivariable dynamics
• Isomorphisms of tensor algebras arising from weighted partial systems
• C*-envelopes of tensor algebras for multivariable dynamics