Unbounded representations of $q$-deformation of Cuntz algebra

TL;DR

This paper investigates a specific q-deformation of the Cuntz algebra, focusing on unbounded *-representations, and provides a classification of all irreducible representations up to unitary equivalence.

Contribution

It introduces well-behaved unbounded *-representations for the q-deformed Cuntz algebra and classifies all irreducible representations.

Findings

Defined well-behaved unbounded *-representations.

Classified all irreducible representations up to unitary equivalence.

Abstract

We study a deformation of the Cuntz-Toeplitz $C^*$-algebra determined by the relations $a_i^*a_i=1+q a_ia_i^*, a_i^*a_j=0$. We define well-behaved unbounded *-representations of the *-algebra defined by relations above and classify all such irreducible representations up to unitary equivalence.