Event Details

Speaker: Réamonn Ó Buachalla (Charles University)

Title: Quantum Groups and One-Cross Bundles

Abstract: We introduce a dual pair of Hopf algebras: the quantum group SUq(2) and the quantized universal enveloping algebra of the Lie algebra sl(2). From this pair, we construct the quantum 2-sphere, which provides a striking q-deformation of the classical geometry of the two-sphere. We then extend this framework to a general pair of Hopf algebras through a new concept - a one-cross bundle. This leads to a broad family of examples that generalise the quantum sphere.