A quantum Frucht's theorem and quantum automorphisms of quantum Cayley graphs

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F25%3A00389446" target="_blank" >RIV/68407700:21230/25:00389446 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1112/plms.70102" target="_blank" >https://doi.org/10.1112/plms.70102</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1112/plms.70102" target="_blank" >10.1112/plms.70102</a>

Result language
angličtina
Original language name
A quantum Frucht's theorem and quantum automorphisms of quantum Cayley graphs
Original language description
We establish a quantum version of Frucht's Theorem, proving that every finite quantum group is the quantum automorphism group of an undirected finite quantum graph. The construction is based on first considering several quantum Cayley graphs of the quantum group in question, and then providing a method to systematically combine them into a single quantum graph with the right symmetry properties. We also show that the dual Gamma of any non-abelian finite group Gamma is 'quantum rigid'. That is, Gamma always admits a quantum Cayley graph whose quantum automorphism group is exactly Gamma.
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
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OECD FORD branch
10101 - Pure mathematics

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

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

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