Noncommutative complex structures on quantum homogeneous spaces

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• 作者：Ré ; amonn Ó ; Buachalla ^{obuachalla@karlin.mff.cuni.cz" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Quantum groups ; Quantum algebra ; Noncommutative geometry
• 刊名：Journal of Geometry and Physics
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：99
• 期：Complete
• 页码：154-173
• 全文大小：491 K

文摘

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 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 framework is applied to the quantum projective spaces endowed with the Heckenberger–Kolb calculus.