Center of the algebra of functions on the quantum group $SU_q(2)$ and related topics

TL;DR

This paper determines the center of the algebra of functions on the quantum group $SU_q(2)$ and related algebras, providing concrete operator-based proofs and exploring additional properties of this quantum group.

Contribution

It explicitly characterizes the center of the algebra of functions on $SU_q(2)$ and related algebras using concrete operator realizations, offering new insights into their structure.

Findings

Center of the algebra of functions on $SU_q(2)$ is explicitly determined.

Centers of related algebras are also characterized.

Provides concrete proofs using operator realizations on Hilbert spaces.

Abstract

The center of the algebra of continuous functions on the quantum group $SU_q(2)$ is determined as well as centers of other related algebras. Several other results concerning this quantum group are given with direct proofs based on concrete realization of these algebras as algebras of operators on a Hilbert space.