Function algebras on the n-dimensional quantum complex space

TL;DR

This paper constructs and classifies a C*-algebra of continuous functions on the n-dimensional quantum complex space, extending classical function algebra concepts into the quantum setting.

Contribution

It introduces a universal C*-algebra for the quantum complex space and classifies its well-behaved Hilbert space representations.

Findings

Classified Hilbert space representations of the defining relations.

Realized representations as multiplication operators on L2-space.

Defined the C*-algebra via operator norm closure of a universal algebra.

Abstract

The paper introduces a (universal) C*-algebra of continuous functions vanishing at infinity on the n-dimensional quantum complex space. To this end, the well-behaved Hilbert space representations of the defining relations are classified. Then these representations are realized by multiplication operators on an L2-space. The C*-algebra of continuous functions vanishing at infinity is defined by considering a *-algebra such that its classical counterpart separates the points of the n-dimensional complex space and by taking the operator norm closure of a universal representation of this algebra.