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
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