Holomorphic Relative Hopf Modules over the Irreducible Quantum Flag Manifolds
| Autor: | Réamonn Ó Buachalla, Fredy Díaz García, Petr Somberg, Karen R. Strung, Andrey Krutov |
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| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Mathematics - Differential Geometry
Pure mathematics Holomorphic function Vector bundle Statistical and Nonlinear Physics Noncommutative geometry Classical limit Mathematics - Algebraic Geometry Differential Geometry (math.DG) Simple (abstract algebra) Mathematics - Quantum Algebra FOS: Mathematics Projective space Quantum Algebra (math.QA) Covariant transformation Algebraic Geometry (math.AG) Mathematics::Symplectic Geometry Mathematical Physics Mathematics Flag (geometry) |
| Popis: | 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 Podle\'s sphere, and subsequent work of Khalkhali and Moatadelro for general quantum projective space. Comment: 22 pages, no figures. This article draws heavily from arXiv:1912.08802 |
| Databáze: | OpenAIRE |
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