The Baum–Connes property for a quantum (semi-)direct product
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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 journal › Journal article › peer-review
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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