Some examples of quantum graphs

DOI10.1007/S11005-022-01603-5arXiv2109.13618MaRDI QIDQ6378775

Publication date: 28 September 2021

Abstract: We summarize different approaches to the theory of quantum graphs and provide several ways to construct concrete examples. First, we classify all undirected quantum graphs on the quantum space

M_{2}

. Secondly, we apply the theory of 2-cocycle deformations to Cayley graphs of abelian groups. This defines a twisting procedure that produces a quantum graph, which is quantum isomorphic to the original one. For instance, we define the anticommutative hypercube graphs. Thirdly, we construct an example of a quantum graph, which is not quantum isomorphic to any classical graph.

Mathematics Subject Classification ID

Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Quantum groups (quantized function algebras) and their representations (20G42) Tannakian categories (18M25) Dagger categories, categorical quantum mechanics (18M40)

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