Quantum isometries and group dual subgroups

Teodor Banica[1]; Jyotishman Bhowmick[2]; Kenny De Commer[1]

  • [1] Department of Mathematics Cergy-Pontoise University 95000 Cergy-Pontoise FRANCE
  • [2] Department of Mathematics University of Oslo Blindern, N-0315 Oslo NORWAY

Annales mathématiques Blaise Pascal (2012)

  • Volume: 19, Issue: 1, page 1-27
  • ISSN: 1259-1734

Abstract

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We study the discrete groups Λ whose duals embed into a given compact quantum group, Λ ^ ⊂ G . In the matrix case G ⊂ U n + the embedding condition is equivalent to having a quotient map Γ U → Λ , where F = { Γ U ∣ U ∈ U 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.

How to cite

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Banica, Teodor, Bhowmick, Jyotishman, and De Commer, Kenny. "Quantum isometries and group dual subgroups." Annales mathématiques Blaise Pascal 19.1 (2012): 1-27. <http://eudml.org/doc/251054>.

@article{Banica2012,
abstract = {We study the discrete groups $\Lambda $ whose duals embed into a given compact quantum group, $\widehat\{\Lambda \}\subset G$. In the matrix case $G\subset U_n^+$ the embedding condition is equivalent to having a quotient map $\Gamma _U\rightarrow \Lambda $, where $F=\lbrace \Gamma _U\mid U\in U_n\rbrace $ 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 $\widehat\{\Lambda \}\subset S_n^+$. 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.},
affiliation = {Department of Mathematics Cergy-Pontoise University 95000 Cergy-Pontoise FRANCE; Department of Mathematics University of Oslo Blindern, N-0315 Oslo NORWAY; Department of Mathematics Cergy-Pontoise University 95000 Cergy-Pontoise FRANCE},
author = {Banica, Teodor, Bhowmick, Jyotishman, De Commer, Kenny},
journal = {Annales mathématiques Blaise Pascal},
keywords = {Quantum isometry; Diagonal subgroup; quantum isometry; diagonal subgroup},
language = {eng},
month = {1},
number = {1},
pages = {1-27},
publisher = {Annales mathématiques Blaise Pascal},
title = {Quantum isometries and group dual subgroups},
url = {http://eudml.org/doc/251054},
volume = {19},
year = {2012},
}

TY - JOUR
AU - Banica, Teodor
AU - Bhowmick, Jyotishman
AU - De Commer, Kenny
TI - Quantum isometries and group dual subgroups
JO - Annales mathématiques Blaise Pascal
DA - 2012/1//
PB - Annales mathématiques Blaise Pascal
VL - 19
IS - 1
SP - 1
EP - 27
AB - We study the discrete groups $\Lambda $ whose duals embed into a given compact quantum group, $\widehat{\Lambda }\subset G$. In the matrix case $G\subset U_n^+$ the embedding condition is equivalent to having a quotient map $\Gamma _U\rightarrow \Lambda $, where $F=\lbrace \Gamma _U\mid U\in U_n\rbrace $ 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 $\widehat{\Lambda }\subset S_n^+$. 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.
LA - eng
KW - Quantum isometry; Diagonal subgroup; quantum isometry; diagonal subgroup
UR - http://eudml.org/doc/251054
ER -

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