Noncommutative complex structures for the full quantum flag manifold of Oq(SU3)

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10513195" target="_blank" >RIV/00216208:11320/25:10513195 - isvavai.cz</a>

Výsledek na webu

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=pduyrUSNCG" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=pduyrUSNCG</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s11005-025-01955-8" target="_blank" >10.1007/s11005-025-01955-8</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Noncommutative complex structures for the full quantum flag manifold of Oq(SU3)

Popis výsledku v původním jazyce

In recent work, Lusztig&apos;s positive root vectors (with respect to a distinguished choice of reduced decomposition of the longest element of the Weyl group) were shown to give a quantum tangent space for every A-series Drinfeld-Jimbo full quantum flag manifold Oq(Fn). Moreover, the associated differential calculus Omega q(0,center dot)(Fn) was shown to have classical dimension, giving a direct q-deformation of the classical anti-holomorphic Dolbeault complex of Fn. Here, we examine in detail the rank two case, namely the full quantum flag manifold of Oq(SU3). In particular, we examine the *-differential calculus associated with Omega q(0,center dot)(F3) and its noncommutative complex geometry. We find that the number of almost-complex structures reduces from 8 (that is 2 to the power of the number of positive roots of sl3) to 4 (that is 2 to the power of the number of simple roots of sl3). Moreover, we show that each of these almost-complex structures is integrable, which is to say, each of them is a complex structure. Finally, we observe that, due to non-centrality of all the non-degenerate coinvariant 2-forms, none of these complex structures admits a left Oq(SU3)-covariant noncommutative K &amp; auml;hler structure.

Název v anglickém jazyce

Noncommutative complex structures for the full quantum flag manifold of Oq(SU3)

Popis výsledku anglicky

In recent work, Lusztig&apos;s positive root vectors (with respect to a distinguished choice of reduced decomposition of the longest element of the Weyl group) were shown to give a quantum tangent space for every A-series Drinfeld-Jimbo full quantum flag manifold Oq(Fn). Moreover, the associated differential calculus Omega q(0,center dot)(Fn) was shown to have classical dimension, giving a direct q-deformation of the classical anti-holomorphic Dolbeault complex of Fn. Here, we examine in detail the rank two case, namely the full quantum flag manifold of Oq(SU3). In particular, we examine the *-differential calculus associated with Omega q(0,center dot)(F3) and its noncommutative complex geometry. We find that the number of almost-complex structures reduces from 8 (that is 2 to the power of the number of positive roots of sl3) to 4 (that is 2 to the power of the number of simple roots of sl3). Moreover, we show that each of these almost-complex structures is integrable, which is to say, each of them is a complex structure. Finally, we observe that, due to non-centrality of all the non-degenerate coinvariant 2-forms, none of these complex structures admits a left Oq(SU3)-covariant noncommutative K &amp; auml;hler structure.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GF24-11728K" target="_blank" >GF24-11728K: Kvantová geometrická teorie reprezentací a nekomutativní fibrace</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2025

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

115

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

40

Strana od-do

68

Kód UT WoS článku

001504591600001

EID výsledku v databázi Scopus

2-s2.0-105007535634