Quantum symmetries of Cayley graphs of abelian groups

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...

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Bibliographic Details
Published in:Glasgow mathematical journal 2023-09, Vol.65 (3), p.655-686, Article 655
Main Author: Gromada, Daniel
Format: Article
Language:English
Subjects:
Algebra
Algorithms
Automorphisms
Fourier transforms
Graphs
Group theory
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Summary: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.
ISSN:0017-0895
1469-509X
DOI:10.1017/S0017089523000198