Induced Representations and the Frobenius Theorem for Finite Quantum Groups

1993 ◽  
pp. 99-113
Author(s):  
Kazimierz Brągiel
Keyword(s):  
Quantum Groups ◽  
Frobenius Theorem ◽  
Induced Representations ◽  
Finite Quantum Groups

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.

scholarly journals Quantum automorphism groups of finite quantum groups are classical

2015 ◽  
Vol 89 ◽  
pp. 32-37 ◽  
Author(s):  
Paweł Kasprzak ◽  
Piotr M. Sołtan ◽  
Stanisław L. Woronowicz
Keyword(s):  
Quantum Groups ◽  
Automorphism Groups ◽  
Finite Quantum Groups

On Finite Quantum Groups at −1

2005 ◽  
Vol 8 (1) ◽  
pp. 11-34 ◽  
Author(s):  
Nicolás Andruskiewitsch ◽  
Sorin Dăscălescu
Keyword(s):  
Quantum Groups ◽  
Finite Quantum Groups

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.

scholarly journals Finite quantum groups and quantum permutation groups

2012 ◽  
Vol 229 (6) ◽  
pp. 3320-3338 ◽  
Author(s):  
Teodor Banica ◽  
Julien Bichon ◽  
Sonia Natale
Keyword(s):  
Quantum Groups ◽  
Permutation Groups ◽  
Finite Quantum Groups
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