Quantum isometries and group dual subgroups
[Isométries quantiques et duaux de groupes]
Annales Mathématiques Blaise Pascal, Tome 19 (2012) no. 1, pp. 1-27.

On étudie les groupes discrets Λ dont les duaux se plongent dans un groupe quantique compact donné, Λ ^G. Dans le cas matriciel GU n + la condition de plongement est équivalente à l’existence d’une application quotient Γ U Λ, où F={Γ U UU n } est une certaine famille de groupes associés à G. On dévéloppe ici un nombre de techniques pour le calcul de F, en partie inspirées pas la classification de Bichon des sous-groupes Λ ^S n + . Ces résultats sont motivés pas la notion de groupe quantique d’isométrie de Goswami, car une variété Riemannienne compacte et connexe ne peut pas avoir des isométries quantiques venant du dual d’un groupe non-abélien.

We study the discrete groups Λ whose duals embed into a given compact quantum group, Λ ^G. In the matrix case GU n + the embedding condition is equivalent to having a quotient map Γ U Λ, where F={Γ U UU n } is a certain family of groups associated to G. We develop here a number of techniques for computing F, partly inspired from Bichon’s classification of group dual subgroups Λ ^S n + . These results are motivated by Goswami’s notion of quantum isometry group, because a compact connected Riemannian manifold cannot have non-abelian group dual isometries.

DOI : https://doi.org/10.5802/ambp.303
Classification : 58J42
Mots clés: Quantum isometry, Diagonal subgroup
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     author = {Teodor Banica and Jyotishman Bhowmick and Kenny De Commer},
     title = {Quantum isometries and group dual subgroups},
     journal = {Annales Math\'ematiques Blaise Pascal},
     pages = {1--27},
     publisher = {Annales math\'ematiques Blaise Pascal},
     volume = {19},
     number = {1},
     year = {2012},
     doi = {10.5802/ambp.303},
     mrnumber = {2978312},
     zbl = {1250.81057},
     language = {en},
     url = {ambp.centre-mersenne.org/item/AMBP_2012__19_1_1_0/}
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Teodor Banica; Jyotishman Bhowmick; Kenny De Commer. Quantum isometries and group dual subgroups. Annales Mathématiques Blaise Pascal, Tome 19 (2012) no. 1, pp. 1-27. doi : 10.5802/ambp.303. https://ambp.centre-mersenne.org/item/AMBP_2012__19_1_1_0/

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