Actions of monoidally equivalent compact quantum groups and applications to probabilistic boundaries

An De Rijdt[1]; Nikolas Vander Vennet[2]

  • [1] Sint-Michielswarande 60 6T4, 1040 Brussel (Belgium)
  • [2] Celestijnenlaan 200 B 3001 Heverlee (Belgium)

Annales de l’institut Fourier (2010)

  • Volume: 60, Issue: 1, page 169-216
  • ISSN: 0373-0956

Abstract

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The notion of monoidal equivalence for compact quantum groups was recently introduced by Bichon, De Rijdt and Vaes. In this paper we prove that there is a natural bijective correspondence between actions of monoidally equivalent quantum groups on unital C * -algebras or on von Neumann algebras. This correspondence turns out to be very useful to obtain the behavior of Poisson and Martin boundaries under monoidal equivalence of quantum groups. Finally, we apply these results to identify the Poisson boundary for the duals of quantum automorphism groups.

How to cite

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De Rijdt, An, and Vander Vennet, Nikolas. "Actions of monoidally equivalent compact quantum groups and applications to probabilistic boundaries." Annales de l’institut Fourier 60.1 (2010): 169-216. <http://eudml.org/doc/116265>.

@article{DeRijdt2010,
abstract = {The notion of monoidal equivalence for compact quantum groups was recently introduced by Bichon, De Rijdt and Vaes. In this paper we prove that there is a natural bijective correspondence between actions of monoidally equivalent quantum groups on unital $C^*$-algebras or on von Neumann algebras. This correspondence turns out to be very useful to obtain the behavior of Poisson and Martin boundaries under monoidal equivalence of quantum groups. Finally, we apply these results to identify the Poisson boundary for the duals of quantum automorphism groups.},
affiliation = {Sint-Michielswarande 60 6T4, 1040 Brussel (Belgium); Celestijnenlaan 200 B 3001 Heverlee (Belgium)},
author = {De Rijdt, An, Vander Vennet, Nikolas},
journal = {Annales de l’institut Fourier},
keywords = {Quantum groups; operator algebras; probability theory; quantum groups},
language = {eng},
number = {1},
pages = {169-216},
publisher = {Association des Annales de l’institut Fourier},
title = {Actions of monoidally equivalent compact quantum groups and applications to probabilistic boundaries},
url = {http://eudml.org/doc/116265},
volume = {60},
year = {2010},
}

TY - JOUR
AU - De Rijdt, An
AU - Vander Vennet, Nikolas
TI - Actions of monoidally equivalent compact quantum groups and applications to probabilistic boundaries
JO - Annales de l’institut Fourier
PY - 2010
PB - Association des Annales de l’institut Fourier
VL - 60
IS - 1
SP - 169
EP - 216
AB - The notion of monoidal equivalence for compact quantum groups was recently introduced by Bichon, De Rijdt and Vaes. In this paper we prove that there is a natural bijective correspondence between actions of monoidally equivalent quantum groups on unital $C^*$-algebras or on von Neumann algebras. This correspondence turns out to be very useful to obtain the behavior of Poisson and Martin boundaries under monoidal equivalence of quantum groups. Finally, we apply these results to identify the Poisson boundary for the duals of quantum automorphism groups.
LA - eng
KW - Quantum groups; operator algebras; probability theory; quantum groups
UR - http://eudml.org/doc/116265
ER -

References

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