# Compact Quantum Homogeneous K\"ahler Spaces

@inproceedings{Das2019CompactQH, title={Compact Quantum Homogeneous K\"ahler Spaces}, author={Biswarup Das and R'eamonn 'O Buachalla and Petr Somberg}, year={2019} }

. Noncommutative K¨ahler structures were recently introduced as an algebraic framework for studying noncommutative complex geometry on quantum homogeneous spaces. In this paper, we introduce the notion of a compact quantum homogeneous K¨ahler space which gives a natural set of compatibility conditions between covariant K¨ahler structures and Woronowicz’s theory of compact quantum groups. Each such object admits a Hilbert space completion possessing a remarkably rich yet tractable structure. The…

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