A noncommutative 2-sphere generated by the quantum complex plane
Volume 98 / 2012
Banach Center Publications 98 (2012), 55-66
MSC: Primary 46L65; Secondary 58B32.
DOI: 10.4064/bc98-0-3
Abstract
S. L. Woronowicz's theory of C*-algebras generated by unbounded elements is applied to $q$-normal operators satisfying the defining relation of the quantum complex plane. The unique non-degenerate C*-algebra of bounded operators generated by a $q$-normal operator is computed and an abstract description is given by using crossed product algebras. If the spectrum of the modulus of the $q$-normal operator is the positive half line, this C*-algebra will be considered as the algebra of continuous functions on the quantum complex plane vanishing at infinity, and its unitization will be viewed as the algebra of continuous functions on a quantum 2-sphere.
