Equivariant Morita equivalences between Podles' spheres

TL;DR

This paper classifies Podles' spheres under equivariant Morita equivalence with quantum SU(2), providing explicit formulas and spectral analysis to understand their relationships and equivalences with quantum projective planes.

Contribution

It establishes the completeness of Podles' spheres under equivariant Morita equivalence and derives explicit formulas for their actions related to quantum projective planes.

Findings

Podles' spheres form a complete family under equivariant Morita equivalence.

Explicit formulas for actions equivalent to quantum projective planes.

Spectral decomposition of a generalized Casimir element used in computations.

Abstract

We show that the family of Podles' spheres is complete under equivariant Morita equivalence (with respect to the action of quantum SU(2)), and determine the associated orbits. We also give explicit formulas for the actions which are equivariantly Morita equivalent with the quantum projective plane. In both cases, the computations are made by examining the localized spectral decomposition of a generalized Casimir element.