Noncommutative Kahler Geometry of the Standard Podles Sphere

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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