Function algebras on a 2-dimensional quantum complex plane

TL;DR

This paper classifies well-behaved representations of the coordinate algebra of a 2D quantum complex plane and defines a C*-algebra representing continuous functions vanishing at infinity on this quantum space.

Contribution

It introduces a classification of representations and constructs a C*-algebra modeling the quantum complex plane, extending noncommutative geometry tools.

Findings

Classification of well-behaved representations

Definition of a C*-algebra for the quantum plane

Modeling of continuous functions vanishing at infinity

Abstract

The well-behaved representations of the coordinate algebra of a 2-dimensional quantum complex plane are classified and a C*-algebra is defined which can be viewed as the algebra of continuous functions on the 2-dimensional quantum complex plane vanishing at infinity.