scholarly journals Property (T), property (F) and residual finiteness for discrete quantum groups

2020 ◽  
Vol 14 (2) ◽  
pp. 567-589
Author(s):  
Angshuman Bhattacharya ◽  
Michael Brannan ◽  
Alexandru Chirvasitu ◽  
Shuzhou Wang
Keyword(s):  
Quantum Groups ◽  
Residual Finiteness ◽  
Property T

Property T for locally compact quantum groups

2015 ◽  
Vol 26 (03) ◽  
pp. 1550024 ◽  
Author(s):  
Xiao Chen ◽  
Chi-Keung Ng
Keyword(s):  
Quantum Group ◽  
Quantum Groups ◽  
Short Paper ◽  
Locally Compact ◽  
C Algebras ◽  
Locally Compact Quantum Groups ◽  
Locally Compact Quantum Group ◽  
Compact Quantum Groups ◽  
Dimensional Irreducible Representation ◽  
Property T

In this short paper, we obtained some equivalent formulations of property T for a general locally compact quantum group 𝔾, in terms of the full quantum group C*-algebras [Formula: see text] and the *-representation of [Formula: see text] associated with the trivial unitary corepresentation (that generalize the corresponding results for locally compact groups). Moreover, if 𝔾 is of Kac type, we show that 𝔾 has property T if and only if every finite-dimensional irreducible *-representation of [Formula: see text] is an isolated point in the spectrum of [Formula: see text] (this also generalizes the corresponding locally compact group result). In addition, we give a way to construct property T discrete quantum groups using bicrossed products.

scholarly journals KAZHDAN'S PROPERTY T FOR DISCRETE QUANTUM GROUPS

2010 ◽  
Vol 21 (01) ◽  
pp. 47-65 ◽  
Author(s):  
PIERRE FIMA
Keyword(s):  
Quantum Group ◽  
Quantum Groups ◽  
Von Neumann Algebra ◽  
Finitely Generated ◽  
Von Neumann ◽  
Property T ◽  
Definition Of ◽  
Simple Definition

We give a simple definition of property T for discrete quantum groups, and prove the basic expected properties: discrete quantum groups with property T are finitely generated and unimodular. Moreover we show that, for "I.C.C." discrete quantum groups, property T is equivalent to Connes' property T for the dual von Neumann algebra. This allows us to give the first example of a property T discrete quantum group which is not a group using the twisting construction.

scholarly journals Quantum G2 categories have property (T)

2016 ◽  
Vol 27 (02) ◽  
pp. 1650015 ◽  
Author(s):  
Corey Jones
Keyword(s):  
Quantum Groups ◽  
Lie Group ◽  
Unitary Representations ◽  
Tensor Categories ◽  
Finite Dimensional ◽  
Positive Formula ◽  
Property T

We show that the rigid [Formula: see text]-tensor categories of finite-dimensional type 1 unitary representations of the quantum groups [Formula: see text] corresponding to the exceptional Lie group [Formula: see text] for positive [Formula: see text] have property (T).

scholarly journals Admissibility Conjecture and Kazhdan's Property (T) for quantum groups

2019 ◽  
Vol 276 (11) ◽  
pp. 3484-3510
Author(s):  
Biswarup Das ◽  
Matthew Daws ◽  
Pekka Salmi
Keyword(s):  
Quantum Groups ◽  
Property T

scholarly journals Around Property (T) for Quantum Groups

2017 ◽  
Vol 353 (1) ◽  
pp. 69-118 ◽  
Author(s):  
Matthew Daws ◽  
Adam Skalski ◽  
Ami Viselter
Keyword(s):  
Quantum Groups ◽  
Property T

scholarly journals Quantum Groups, Property (T), and Weak Mixing

2017 ◽  
Vol 360 (3) ◽  
pp. 1043-1059 ◽  
Author(s):  
Michael Brannan ◽  
David Kerr
Keyword(s):  
Quantum Groups ◽  
Weak Mixing ◽  
Property T

scholarly journals Property (T) discrete quantum groups and subfactors with triangle presentations

2019 ◽  
Vol 345 ◽  
pp. 382-428
Author(s):  
Stefaan Vaes ◽  
Matthias Valvekens
Keyword(s):  
Quantum Groups ◽  
Property T
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