Interactions and dynamical systems of type (n,m) - A case study

TL;DR

This paper demonstrates that the C*-algebra of a universal (n,m)-dynamical system can be represented as a crossed product relative to an interaction on a commutative C*-algebra, highlighting a specific structural property.

Contribution

It establishes a connection between (n,m)-dynamical systems and crossed products via interactions, clarifying their algebraic structure and independence from interaction groups.

Findings

C*-algebra of (n,m)-dynamical system is Morita-Rieffel equivalent to a crossed product

The involved interaction is not part of an interaction group

Provides a new perspective on the structure of these dynamical systems

Abstract

We prove that the C*-algebra of the universal (n,m)-dynamical system may be obtained, up to Morita-Rieffel equivalence, as the crossed-product relative to an interaction on a commutative C*-algebra. The interaction involved is shown not to be part of an interaction group.