Gauge transformations on quantum principal bundles

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10509030" target="_blank" >RIV/00216208:11320/25:10509030 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.22323/1.490.0310" target="_blank" >http://dx.doi.org/10.22323/1.490.0310</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.22323/1.490.0310" target="_blank" >10.22323/1.490.0310</a>

Result language
angličtina
Original language name
Gauge transformations on quantum principal bundles
Original language description
We understand quantum principal bundle as faithfully flat Hopf–Galois extensions, with a structureHopf algebra coacting on a total space algebra and with base algebra given by the coinvariantelements. To endow such bundles with a compatible differential structure, one requires the coactionto extend as a morphism of differential graded algebras. This leads to an exact noncommutativeAtiyah sequence, a graded Hopf–Galois extension of differential forms and a canonical braidingon total space forms such that the latter are graded-braided commutative. We recall this approachto noncommutative differential geometry and further discuss the extension of quantum gaugetransformations, in the sense of Brzeziński, to differential forms. In this way we obtain an actionof quantum gauge transformations on connections of the quantum principal bundle and theircurvature. Explicit examples, such as the noncommutative 2-torus, the quantum Hopf fibrationand smash product algebras are discussed
Czech name
—
Czech description
—

Project
<a href="/en/project/GN24-11324I" target="_blank" >GN24-11324I: Braided differential geometry and homotopy algebras</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

Similar results(10)