A tensor product of representations of Cuntz algebras

TL;DR

This paper introduces a new nonsymmetric tensor product for representations of Cuntz algebras, providing explicit decomposition formulas and analyzing their implications for endomorphism properties.

Contribution

It presents a novel associative tensor product for Cuntz algebra representations and derives explicit decomposition formulas, advancing understanding of their structure.

Findings

Explicit decomposition formulas for tensor products of permutative representations

Application of formulas to analyze properties of endomorphisms

Establishment of a nonsymmetric, associative tensor product framework

Abstract

We introduce a nonsymmetric, associative tensor product among representations of Cuntz algebras by using embeddings. We show the decomposition formulae of tensor products for permutative representations explicitly We apply decomposition formulae to determine properties of endomorphisms.