Bimodule Connections for Relative Line Modules over the Irreducible Quantum Flag Manifolds

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10455805" target="_blank" >RIV/00216208:11320/22:10455805 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=WeZ120I3iN" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=WeZ120I3iN</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.3842/SIGMA.2022.070" target="_blank" >10.3842/SIGMA.2022.070</a>

Result language
angličtina
Original language name
Bimodule Connections for Relative Line Modules over the Irreducible Quantum Flag Manifolds
Original language description
It was recently shown (by the second author and Di ' az Garci ' a, Krutov, Somberg, and Strung) that every relative line module over an irreducible quantum flag manifold (9q(G/LS) admits a unique (9q(G)-covariant connection with respect to the Heckenberger- Kolb differential calculus ohm 1q(G/LS). In this paper we show that these connections are bimodule connections with an invertible associated bimodule map. This is proved by applying general results of Beggs and Majid, on principal connections for quantum principal bundles, to the quantum principal bundle presentation of the Heckenberger-Kolb calculi recently constructed by the authors and Di ' az Garci ' a. Explicit presentations of the associated bimodule maps are given first in terms of generalised quantum determinants, then in terms of the FRT presentation of the algebra (9q(G), and finally in terms of Takeuchi's categorical equivalence for relative Hopf modules.
Czech name
—
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
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical
Symmetry, Integrability and Geometry - Methods and Applications
ISSN
1815-0659
e-ISSN
—
Volume of the periodical
18
Issue of the periodical within the volume
070
Country of publishing house
UA - UKRAINE
Number of pages
21
Pages from-to
070
UT code for WoS article
000868891500001
EID of the result in the Scopus database
2-s2.0-85139471597

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