The Baum–Connes property for a quantum (semi-)direct product

Research output: Contribution to journalJournal articlepeer-review

Standard

The Baum–Connes property for a quantum (semi-)direct product. / Martos, Rubén.

In: Journal of Noncommutative Geometry, Vol. 13, No. 4, 2019, p. 1295-1357.

Research output: Contribution to journalJournal articlepeer-review

Harvard

Martos, R 2019, 'The Baum–Connes property for a quantum (semi-)direct product', Journal of Noncommutative Geometry, vol. 13, no. 4, pp. 1295-1357. https://doi.org/10.4171/JNCG/348

APA

Martos, R. (2019). The Baum–Connes property for a quantum (semi-)direct product. Journal of Noncommutative Geometry, 13(4), 1295-1357. https://doi.org/10.4171/JNCG/348

Vancouver

Martos R. The Baum–Connes property for a quantum (semi-)direct product. Journal of Noncommutative Geometry. 2019;13(4):1295-1357. https://doi.org/10.4171/JNCG/348

Author

Martos, Rubén. / The Baum–Connes property for a quantum (semi-)direct product. In: Journal of Noncommutative Geometry. 2019 ; Vol. 13, No. 4. pp. 1295-1357.

Bibtex

@article{4dacb014e9594d2497be75f86dc9fdb6,
title = "The Baum–Connes property for a quantum (semi-)direct product",
abstract = "The well known “associativity property” of the crossed product by a semi-direct product of discrete groups is generalized into the context of discrete quantum groups. This decomposition allows to define an appropriate triangulated functor relating the Baum–Connes property for the quantum semi-direct product to the Baum–Connes property for the discrete quantum groups involved in the construction. The corresponding stability result for the Baum–Connes property generalizes the result [5] of J. Chabert for a quantum semi-direct product under torsion-freeness assumption. The K-amenability connexion between the discrete quantum groups involved in the construction is investigated as well as the torsion phenomena. The analogous strategy can be applied for the dual of a quantum direct product. In this case, we obtain, in addition, a connection with the K{\"u}nneth formula, which is the quantum counterpart to the result [7] of J. Chabert, S. Echterhoff and H. Oyono-Oyono. Again the K-amenability connexion between the discrete quantum groups involved in the construction is investigated as well as the torsion phenomena.",
keywords = "Baum–Connes conjecture, Divisible discrete quantum subgroups, K-amenability, K{\"u}nneth formula, Quantum direct product, Quantum groups, Quantum semi-direct product, Torsion",
author = "Rub{\'e}n Martos",
year = "2019",
doi = "10.4171/JNCG/348",
language = "English",
volume = "13",
pages = "1295--1357",
journal = "Journal of Noncommutative Geometry",
issn = "1661-6952",
publisher = "European Mathematical Society Publishing House",
number = "4",

}

RIS

TY - JOUR

T1 - The Baum–Connes property for a quantum (semi-)direct product

AU - Martos, Rubén

PY - 2019

Y1 - 2019

N2 - The well known “associativity property” of the crossed product by a semi-direct product of discrete groups is generalized into the context of discrete quantum groups. This decomposition allows to define an appropriate triangulated functor relating the Baum–Connes property for the quantum semi-direct product to the Baum–Connes property for the discrete quantum groups involved in the construction. The corresponding stability result for the Baum–Connes property generalizes the result [5] of J. Chabert for a quantum semi-direct product under torsion-freeness assumption. The K-amenability connexion between the discrete quantum groups involved in the construction is investigated as well as the torsion phenomena. The analogous strategy can be applied for the dual of a quantum direct product. In this case, we obtain, in addition, a connection with the Künneth formula, which is the quantum counterpart to the result [7] of J. Chabert, S. Echterhoff and H. Oyono-Oyono. Again the K-amenability connexion between the discrete quantum groups involved in the construction is investigated as well as the torsion phenomena.

AB - The well known “associativity property” of the crossed product by a semi-direct product of discrete groups is generalized into the context of discrete quantum groups. This decomposition allows to define an appropriate triangulated functor relating the Baum–Connes property for the quantum semi-direct product to the Baum–Connes property for the discrete quantum groups involved in the construction. The corresponding stability result for the Baum–Connes property generalizes the result [5] of J. Chabert for a quantum semi-direct product under torsion-freeness assumption. The K-amenability connexion between the discrete quantum groups involved in the construction is investigated as well as the torsion phenomena. The analogous strategy can be applied for the dual of a quantum direct product. In this case, we obtain, in addition, a connection with the Künneth formula, which is the quantum counterpart to the result [7] of J. Chabert, S. Echterhoff and H. Oyono-Oyono. Again the K-amenability connexion between the discrete quantum groups involved in the construction is investigated as well as the torsion phenomena.

KW - Baum–Connes conjecture

KW - Divisible discrete quantum subgroups

KW - K-amenability

KW - Künneth formula

KW - Quantum direct product

KW - Quantum groups

KW - Quantum semi-direct product

KW - Torsion

UR - http://www.scopus.com/inward/record.url?scp=85079200682&partnerID=8YFLogxK

U2 - 10.4171/JNCG/348

DO - 10.4171/JNCG/348

M3 - Journal article

AN - SCOPUS:85079200682

VL - 13

SP - 1295

EP - 1357

JO - Journal of Noncommutative Geometry

JF - Journal of Noncommutative Geometry

SN - 1661-6952

IS - 4

ER -

ID: 238955124