O* - Dynamical Systems and * - Derivations of Unbounded Operator Algebras

1999 ◽  
Vol 204 (1) ◽  
pp. 5-28 ◽  
Author(s):  
J - P. Antoine ◽  
A. Inoue ◽  
C. Trapani
Keyword(s):  
Dynamical Systems ◽  
Unbounded Operator ◽  
Operator Algebras

Type classification of extreme quantized characters

2019 ◽  
Vol 41 (2) ◽  
pp. 593-605
Author(s):  
RYOSUKE SATO
Keyword(s):  
Dynamical Systems ◽  
Quantum Groups ◽  
Asymptotic Representation ◽  
Operator Algebras ◽  
Complete Solution ◽  
Unitary Groups ◽  
Inductive System ◽  
Von Neumann ◽  
Type Classification

The notion of quantized characters was introduced in our previous paper as a natural quantization of characters in the context of asymptotic representation theory for quantum groups. As in the case of ordinary groups, the representation associated with any extreme quantized character generates a von Neumann factor. From the viewpoint of operator algebras (and measurable dynamical systems), it is natural to ask what is the Murray–von Neumann–Connes type of the resulting factor. In this paper, we give a complete solution to this question when the inductive system is of quantum unitary groups $U_{q}(N)$.

scholarly journals Compact group actions on operator algebras and their spectra

2020 ◽  
Vol 126 (2) ◽  
pp. 276-292
Author(s):  
Costel Peligrad
Keyword(s):  
Fixed Point ◽  
Dynamical Systems ◽  
Compact Group ◽  
Spectral Properties ◽  
Operator Algebras ◽  
Abelian Groups ◽  
Group Actions ◽  
Algebraic Properties

We consider a class of dynamical systems with compact non-abelian groups that include C*-, W*- and multiplier dynamical systems. We prove results that relate the algebraic properties such as simplicity or primeness of the fixed point algebras to the spectral properties of the action, including the Connes and strong Connes spectra.

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