On the Construction of Quantum Homogeneous Spaces from ∗ -Galois Objects

Abstract

In this note we construct bi- ∗ -Galois objects linking the quantized universal enveloping algebras associated to the Lie groups SU(2), E(2) and SU(1, 1), where E(2) denotes the Lie group of Euclidian transformations of the plane, and we show how one can create (formal) quantum homogeneous spaces for these quantum groups by integrating the associated Miyashita-Ulbrich action on certain subquotient ∗ -algebras.