Holomorphic Relative Hopf Modules over the Irreducible Quantum Flag Manifolds

被引：0
作者：
Fredy Díaz García
Andrey Krutov
Réamonn Ó Buachalla
Petr Somberg
Karen R. Strung
机构：
[1] Universidad Nacional Autónoma de México,Centro de Ciencias Matemáticas
[2] University of Zagreb,Department of Mathematics
[3] Czech Academy of Sciences,Institute of Mathematics
[4] Independent University of Moscow,Département de Mathématiques, Faculté des sciences
[5] Université Libre de Bruxelles,undefined
[6] Mathematical Institute of Charles University,undefined
来源：
Letters in Mathematical Physics | 2021年 / 111卷
关键词：
Quantum groups; Noncommutative geometry; Quantum principal bundles; Quantum flag manifolds; Complex geometry; Holomorphic vector bundles; 46L87; 81R60; 81R50; 17B37; 16T05;
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摘要：
We construct covariant q-deformed holomorphic structures for all finitely generated relative Hopf modules over the irreducible quantum flag manifolds endowed with their Heckenberger–Kolb calculi. In the classical limit, these reduce to modules of sections of holomorphic homogeneous vector bundles over irreducible flag manifolds. For the case of simple relative Hopf modules, we show that this covariant holomorphic structure is unique. This generalises earlier work of Majid, Khalkhali, Landi, and van Suijlekom for line modules of the Podleś sphere, and subsequent work of Khalkhali and Moatadelro for general quantum projective space.
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