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arXiv · 1108.2374

Noncommutative Complex Structures on Quantum Homogeneous Spaces

Réamonn Ó Buachalla
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Abstract

A new framework for noncommutative complex geometry on quantum homogeneous spaces is introduced. The main ingredients used are covariant differential calculi and Takeuchi's categorical equivalence for faithfully flat quantum homogeneous spaces. A number of basic results are established, producing a simple set of necessary and sufficient conditions for noncommutative complex structures to exist. Throughout, the family of quantum projective spaces, endowed with the Heckenberger--Kolb calculus, is taken as the motivating set of examples.

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Réamonn Ó Buachalla. 2011-08-11. Noncommutative Complex Structures on Quantum Homogeneous Spaces. https://arxiv.org/abs/1108.2374

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