Noncommutative Kahler Geometry of the Standard Podles Sphere

Abstract

Building on the now established presentation of the standard Podles sphere as an example of a noncommutative complex structure, we investigate how its classical Kahler geometry behaves under $q$-deformation. Discussed are noncommutative versions of Hodge decomposition, Lefschetz decomposition, the Kahler identities, and the refinement of de Rham cohomology by Dolbeault cohomology

References in corpus (2)

• Gauged Laplacians on quantum Hopf bundles
• The resolvent cocycle in twisted cyclic cohomology and a local index formula for the Podles sphere