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

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Noncommutative complex structures for the full quantum flag manifold of Oq(SU3)
Original language description
In recent work, Lusztig'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 & auml;hler structure.
Czech name
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Czech description
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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

Project
<a href="/en/project/GF24-11728K" target="_blank" >GF24-11728K: Quantum geometric representation theory and noncommutative fibrations</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2025
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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