A tensor product of representations of UHF algebras arising from Kronecker products

TL;DR

This paper introduces a new non-symmetric tensor product for representations of UHF algebras based on Kronecker products, providing tensor product formulas for GNS representations and illustrating with examples.

Contribution

It presents a novel tensor product construction for UHF algebra representations using Kronecker products, expanding the understanding of their structure.

Findings

Derived tensor product formulas for GNS representations

Provided explicit examples illustrating the new tensor product

Established foundational properties of the non-symmetric tensor product

Abstract

We introduce a non-symmetric tensor product of representations of UHF algebras by using Kronecker products of matrices. We prove tensor product formulae of GNS representations by product states and show examples.