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
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Czech description
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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