Deformation by Dual Unitary Cocycles and Generalized Fixed Point Algebra for Quantum Group Actions

2015 ◽  
pp. 57-67
Author(s):  
Debashish Goswami ◽  
Soumalya Joardar
Keyword(s):  
Fixed Point ◽  
Quantum Group ◽  
Group Actions ◽  
Quantum Group Actions ◽  
Fixed Point Algebra

scholarly journals A REMARK ON QUANTUM GROUP ACTIONS AND NUCLEARITY

2002 ◽  
Vol 14 (07n08) ◽  
pp. 787-796 ◽  
Author(s):  
S. DOPLICHER ◽  
R. LONGO ◽  
J. E. ROBERTS ◽  
L. ZSIDÓ
Keyword(s):  
Fixed Point ◽  
Quantum Group ◽  
Haar Measure ◽  
Group Actions ◽  
Compact Quantum Group ◽  
C Algebra ◽  
Quantum Group Actions

Let H be a compact quantum group with faithful Haar measure and bounded counit. If α is an action of H on a C*- algebra A, we show that A is nuclear if and only if the fixed-point subalgebra Aα is nuclear. As a consequence H is a nuclear C*-algebra.

Morita equivalences between fixed point algebras and crossed products

1999 ◽  
Vol 125 (1) ◽  
pp. 43-52 ◽  
Author(s):  
CHI-KEUNG NG
Keyword(s):  
Fixed Point ◽  
Quantum Group ◽  
Type Theorem ◽  
Compact Quantum Group ◽  
Crossed Product ◽  
Crossed Products ◽  
Morita Equivalent ◽  
Fixed Point Algebra

In this paper, we will prove that if A is a C*-algebra with an effective coaction ε by a compact quantum group, then the fixed point algebra and the reduced crossed product are Morita equivalent. As an application, we prove an imprimitivity type theorem for crossed products of coactions by discrete Kac C*-algebras.

Quantum Group Actions on the Cuntz Algebra

2000 ◽  
Vol 1 (6) ◽  
pp. 1097-1122 ◽  
Author(s):  
A.L. Carey ◽  
A. Paolucci ◽  
R.B. Zhang
Keyword(s):  
Quantum Group ◽  
Group Actions ◽  
Cuntz Algebra ◽  
Quantum Group Actions
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