The characteristic square of a factor and the cocycle conjugacy of discrete group actions on factors

1998 ◽  
Vol 132 (2) ◽  
pp. 331-380 ◽  
Author(s):  
Yoshikazu Katayama ◽  
Colin E. Sutherland ◽  
Masamichi Takesaki
Keyword(s):  
Discrete Group ◽  
Group Actions ◽  
Cocycle Conjugacy

The Baum–Connes Conjecture and Discrete Group Actions on Trees

K-Theory ◽  
1999 ◽  
Vol 17 (4) ◽  
pp. 303-318 ◽  
Author(s):  
Jean-louis Tu
Keyword(s):  
Discrete Group ◽  
Group Actions

A CONTINUUM OF DISCRETE GROUP ACTIONS ON A FERMIONIC FACTOR

1993 ◽  
Vol 44 (3) ◽  
pp. 339-343 ◽  
Author(s):  
KAZUYUKI SAITÔ ◽  
J. D. MAITLAND WRIGHT
Keyword(s):  
Discrete Group ◽  
Group Actions

Poly-${\mathbb{Z}}$ Group Actions on Kirchberg Algebras I

2019 ◽  
Author(s):  
Masaki Izumi ◽  
Hiroki Matui
Keyword(s):  
Group Actions ◽  
Complete Classification ◽  
Cocycle Conjugacy ◽  
Fundamental Theorems

Abstract Toward the complete classification of poly-${\mathbb{Z}}$ group actions on Kirchberg algebras, we prove several fundamental theorems that are used in the classification. In addition, as an application of them, we classify outer actions of poly-${\mathbb{Z}}$ groups of Hirsch length not greater than three on unital Kirchberg algebras up to $KK$-trivial cocycle conjugacy.

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