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Quantum symmetries of Cayley graphs of abelian groups

Part of: Graph theory Linear algebraic groups and related topics

Published online by Cambridge University Press:  12 October 2023

Daniel Gromada Open the ORCID record for Daniel Gromada [Opens in a new window]
Daniel Gromada*
Affiliation:
Department of Mathematics, Faculty of Electrical Engineering, Czech Technical University in Prague, Praha, Czechia
*
Email: gromadan@fel.cvut.cz
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Abstract

We study Cayley graphs of abelian groups from the perspective of quantum symmetries. We develop a general strategy for determining the quantum automorphism groups of such graphs. Applying this procedure, we find the quantum symmetries of the halved cube graph, the folded cube graph, and the Hamming graphs.

Keywords

Cayley graphhypercube graphHamming graphquantum symmetry

MSC classification

Primary: 20G42: Quantum groups (quantized function algebras) and their representations
Secondary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.)
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 65 , Issue 3 , September 2023 , pp. 655 - 686
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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