Positive line modules over the irreducible quantum flag manifolds

Kód výsledku v 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>

Nalezeny alternativní kódy

RIV/00216208:11320/22:10453234

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Positive line modules over the irreducible quantum flag manifolds

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Positive line modules over the irreducible quantum flag manifolds

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GJ20-17488Y" target="_blank" >GJ20-17488Y: Aplikace klasifikace C*-algeber: dynamika, geometrie a jejich kvantové analogie</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

Letters in Mathematical Physics

ISSN

0377-9017

e-ISSN

1573-0530

Svazek periodika

112

Číslo periodika v rámci svazku

6

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

33

Strana od-do

123

Kód UT WoS článku

000895594800001

EID výsledku v databázi Scopus

2-s2.0-85143605057