scholarly journals EMBEDDING ERGODIC ACTIONS OF COMPACT QUANTUM GROUPS ON C*-ALGEBRAS INTO QUOTIENT SPACES

2007 ◽  
Vol 18 (02) ◽  
pp. 137-164 ◽  
Author(s):  
CLAUDIA PINZARI
Keyword(s):  
Quantum Groups ◽  
Reciprocity Theorem ◽  
Sufficient Condition ◽  
Alternative Definition ◽  
Topological Transitivity ◽  
Frobenius Reciprocity ◽  
Induced Representations ◽  
C Algebras ◽  
Quotient Spaces ◽  
Compact Quantum Groups

The notion of compact quantum subgroup is revisited and an alternative definition is given. Induced representations are considered and a Frobenius reciprocity theorem is obtained. A relationship between ergodic actions of compact quantum groups on C*-algebras and topological transitivity is investigated. A sufficient condition for embedding such actions in quantum quotient spaces is obtained.

GEOMETRY OF QUANTUM HOMOGENEOUS VECTOR BUNDLES AND REPRESENTATION THEORY OF QUANTUM GROUPS I

1999 ◽  
Vol 11 (05) ◽  
pp. 533-552 ◽  
Author(s):  
A. R. GOVER ◽  
R. B. ZHANG
Keyword(s):  
Representation Theory ◽  
Finite Type ◽  
Quantum Groups ◽  
Vector Bundles ◽  
Homogeneous Spaces ◽  
Projective Modules ◽  
Geometrical Structures ◽  
Induced Representations ◽  
Compact Quantum Groups ◽  
Homogeneous Vector

Quantum homogeneous vector bundles are introduced in the context of Woronowicz type compact quantum groups. The bundles carry natural topologies, and their sections furnish finite type projective modules over algebras of functions on quantum homogeneous spaces. Further properties of the quantum homogeneous vector bundles are investigated, and applied to the study of the geometrical structures of induced representations of quantum groups.

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 Induction for locally compact quantum groups revisited

2019 ◽  
Vol 150 (2) ◽  
pp. 1071-1093
Author(s):  
Mehrdad Kalantar ◽  
Paweł Kasprzak ◽  
Adam Skalski ◽  
Piotr M. Sołtan
Keyword(s):  
Quantum Groups ◽  
General Setting ◽  
Locally Compact ◽  
Induced Representations ◽  
Open Quantum ◽  
Locally Compact Quantum Groups ◽  
Weak Containment ◽  
Compact Quantum Groups

AbstractIn this paper, we revisit the theory of induced representations in the setting of locally compact quantum groups. In the case of induction from open quantum subgroups, we show that constructions of Kustermans and Vaes are equivalent to the classical, and much simpler, construction of Rieffel. We also prove in general setting the continuity of induction in the sense of Vaes with respect to weak containment.

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