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Positive line modules over the irreducible quantum flag manifolds

The result's identifiers

  • Result code in IS VaVaI

    <a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F22%3A00565240" target="_blank" >RIV/67985840:_____/22:00565240 - isvavai.cz</a>

  • Alternative codes found

    RIV/00216208:11320/22:10453234

  • Result on the web

    <a href="https://doi.org/10.1007/s11005-022-01619-x" target="_blank" >https://doi.org/10.1007/s11005-022-01619-x</a>

  • DOI - Digital Object Identifier

    <a href="http://dx.doi.org/10.1007/s11005-022-01619-x" target="_blank" >10.1007/s11005-022-01619-x</a>

Alternative languages

  • Result language

    angličtina

  • Original language name

    Positive line modules over the irreducible quantum flag manifolds

  • Original language description

    Noncommutative Kähler structures were recently introduced as a framework for studying noncommutative Kähler geometry on quantum homogeneous spaces. It was subsequently observed that the notion of a positive vector bundle directly generalises to this setting, as does the Kodaira vanishing theorem. In this paper, by restricting to covariant Kähler structures of irreducible type (those having an irreducible space of holomorphic 1-forms) we provide simple cohomological criteria for positivity, allowing one to avoid explicit curvature calculations. These general results are applied to our motivating family of examples, the irreducible quantum flag manifolds Oq(G/LS). Building on the recently established noncommutative Borel–Weil theorem, every relative line module over Oq(G/LS) can be identified as positive, negative, or flat, and it is then concluded that each Kähler structure is of Fano type.

  • Czech name

  • Czech description

Classification

  • Type

    J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database

  • CEP classification

  • OECD FORD branch

    10101 - Pure mathematics

Result continuities

  • Project

    <a href="/en/project/GJ20-17488Y" target="_blank" >GJ20-17488Y: Applications of C*-algebra classification: dynamics, geometry, and their quantum analogues</a><br>

  • Continuities

    I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Others

  • Publication year

    2022

  • Confidentiality

    S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Data specific for result type

  • Name of the periodical

    Letters in Mathematical Physics

  • ISSN

    0377-9017

  • e-ISSN

    1573-0530

  • Volume of the periodical

    112

  • Issue of the periodical within the volume

    6

  • Country of publishing house

    NL - THE KINGDOM OF THE NETHERLANDS

  • Number of pages

    33

  • Pages from-to

    123

  • UT code for WoS article

    000895594800001

  • EID of the result in the Scopus database

    2-s2.0-85143605057