Quantum symmetries of Cayley graphs of abelian groups

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.

arXiv comment35 pages; corrected §6.2

References in corpus (10)

• Quantum Symmetry Groups of Finite Spaces
• The hyperoctahedral quantum group
• Eigenvalues of Cayley graphs
• Quantum groups and Fuss-Catalan algebras
• Quantum automorphisms of folded cube graphs
• On the quantum symmetry of distance-transitive graphs
• Study of quantum symmetries for vertex-transitive graphs using intertwiner spaces
• Generating linear categories of partitions
• Free quantum analogue of Coxeter group $D_4$
• The Frucht property in the quantum group setting

Cited by in corpus (3)

• Some examples of quantum graphs
• Presentations of projective quantum groups
• Duals of finite quantum permutation groups