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View all- Faroß NWeber M(2024)A Concrete Model for the Quantum Permutation Group on 4 PointsExperimental Mathematics10.1080/10586458.2024.2337232(1-14)Online publication date: 13-Apr-2024
Existence of Quantum Symmetries for Graphs on Up to Seven Vertices: A Computer based Approach
Authors: 
Viktor Levandovskyy, Christian Eder, Andreas Steenpass, Simon Schmidt, Julien Schanz, Moritz WeberAuthors Info & Claims
Viktor Levandovskyy, Christian Eder, Andreas Steenpass, Simon Schmidt, Julien Schanz, Moritz WeberAuthors Info & ClaimsPages 311 - 318
Abstract
The symmetries of a finite graph are described by its automorphism group; in the setting of Woronowicz's quantum groups, a notion of a quantum automorphism group has been defined by Banica capturing the quantum symmetries of the graph. In general, there are more quantum symmetries than symmetries and it is a non-trivial task to determine when this is the case for a given graph: The question is whether or not the associative algebra associated to the quantum automorphism group is commutative. We use noncommutative Gröbner bases in order to tackle this problem; the implementation uses Gap and Singular:Letterplace. We determine the existence of quantum symmetries for all connected, undirected graphs without multiple edges and without self-edges, for up to seven vertices. As an outcome, we infer within our regime that a classical automorphism group of order one or two is an obstruction for the existence of quantum symmetries.
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- Existence of Quantum Symmetries for Graphs on Up to Seven Vertices: A Computer based Approach
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Published: 05 July 2022
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View all- Faroß NWeber M(2024)A Concrete Model for the Quantum Permutation Group on 4 PointsExperimental Mathematics10.1080/10586458.2024.2337232(1-14)Online publication date: 13-Apr-2024
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