Quantum permutation groups - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2023

Quantum permutation groups

Teo Banica
  • Fonction : Auteur
  • PersonId : 1045618

Résumé

The permutation group $S_N$ has a quantum analogue $S_N^+$, which is infinite at $N\geq4$. We review the known facts regarding $S_N^+$, and notably its easiness property, Weingarten calculus, and the isomorphism $S_4^+=SO_3^{-1}$ and its consequences. We discuss then the structure of the closed subgroups $G\subset S_N^+$, and notably of the quantum symmetry groups of finite graphs $G^+(X)\subset S_N^+$, with particular attention to the quantum reflection groups $H_N^{s+}$. We also discuss, more generally, the quantum symmetry groups $S_F^+$ of the finite quantum spaces $F$, and their closed subgroups $G\subset S_F^+$, with particular attention to the quantum graph case, and to quantum reflection groups.
Fichier principal
Vignette du fichier
qp.pdf (1.63 Mo) Télécharger le fichier
Origine Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03319772 , version 1 (13-08-2021)
hal-03319772 , version 2 (07-12-2021)
hal-03319772 , version 3 (14-04-2022)
hal-03319772 , version 4 (05-03-2023)
hal-03319772 , version 5 (12-06-2023)
hal-03319772 , version 6 (07-08-2024)

Identifiants

  • HAL Id : hal-03319772 , version 5

Citer

Teo Banica. Quantum permutation groups. 2023. ⟨hal-03319772v5⟩
61 Consultations
493 Téléchargements

Partager

More