Quantum automorphism groups of small metric spaces
By T. Banica. 2003
120 citations recorded by the source corpus.
To any ?nite metric space X we associate the universal Hopf C*-algebra H coacting on X. We prove that spaces X having at most 7 points fall into one of the following classes: (1) the coaction of H is not transitive; (2) H is the algebra of functions on the automorphism group of X; (3) X is a simplex and H corresponds to a Temperley?Lieb algebra; (4) X is a product of simplices and H corresponds to a Fuss?Catalan algebra.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/801270addedee5d9a66eb4b596b04773c5bf9249
How researchers see this paper
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In Algebra and Number Theory
- Julien Bichon
- T. Banica
- Benoît Collins
- Michael Brannan
- Roland Speicher
- Stephen J. Curran
- Moritz Weber
- Pierre Tarrago
In Geometry and Topology
- T. Banica
- Julien Bichon
- Benoît Collins
- Roland Speicher
- Michael Brannan
- Moritz Weber
- Amaury Freslon
- Stephen J. Curran
In Mathematical Physics
- T. Banica
- Julien Bichon
- Benoît Collins
- Roland Speicher
- Michael Brannan
- Moritz Weber
- Amaury Freslon
- Stephen J. Curran
Citations in the corpus
- Quantum permutation groups: a survey (2006, methodology): “This number is n = 7, 8, 9, 11 in the papers [2], [3], [4], [5].”
- Quantum automorphism groups of vertex-transitive graphs of order ≤ 11 (2006, methodology): “It is known from [2] that the n-cycle with n 6= 4 has quantum symmetry group Dn.”