Crossed Product Algebras and the Homology of Certain p-Adic and Adélic Dynamical Systems

K-Theory ◽  
2000 ◽  
Vol 21 (1) ◽  
pp. 1-23 ◽  
Author(s):  
Eric Leichtnam ◽  
Victor Nistor
Keyword(s):  
Dynamical Systems ◽  
Crossed Product ◽  
Crossed Product Algebras

Smooth crossed product of minimal unique ergodic diffeomorphisms of a manifold and cyclic cohomology

2019 ◽  
Vol 11 (03) ◽  
pp. 739-751 ◽  
Author(s):  
Hongzhi Liu
Keyword(s):  
Dynamical Systems ◽  
Cyclic Cohomology ◽  
Crossed Product ◽  
Classification Theory ◽  
Crossed Product Algebra ◽  
Product Algebra ◽  
Crossed Product Algebras

Different diffeomorphisms can give the same [Formula: see text] crossed product algebra. Our main purpose is to show that we can still classify dynamical systems with some appropriate smooth crossed product algebras when their corresponding [Formula: see text] crossed product algebras are isomorphic. For this purpose, we construct two minimal unique ergodic diffeomorphisms [Formula: see text] and [Formula: see text] of [Formula: see text]. The [Formula: see text] algebras classification theory, smooth crossed product algebras considered by R. Nest and cyclic cohomology are used to show that [Formula: see text] and [Formula: see text] give the same [Formula: see text] algebra and induce different smooth crossed product algebras.

Primes of Gauss Extensions Over Crossed Product Algebras

2012 ◽  
Vol 40 (6) ◽  
pp. 1951-1973 ◽  
Author(s):  
H. H. Brungs ◽  
H. Marubayashi ◽  
E. Osmanagic
Keyword(s):  
Crossed Product ◽  
Crossed Product Algebras

On simplicity of intermediate -algebras

2019 ◽  
Vol 40 (12) ◽  
pp. 3181-3187
Author(s):  
TATTWAMASI AMRUTAM ◽  
MEHRDAD KALANTAR
Keyword(s):  
Dynamical Systems ◽  
Simple Group ◽  
Crossed Product ◽  
Simple Groups ◽  
Stationary States ◽  
Compact Spaces ◽  
Link Type ◽  
One To One

We prove simplicity of all intermediate $C^{\ast }$-algebras $C_{r}^{\ast }(\unicode[STIX]{x1D6E4})\subseteq {\mathcal{B}}\subseteq \unicode[STIX]{x1D6E4}\ltimes _{r}C(X)$ in the case of minimal actions of $C^{\ast }$-simple groups $\unicode[STIX]{x1D6E4}$ on compact spaces $X$. For this, we use the notion of stationary states, recently introduced by Hartman and Kalantar [Stationary $C^{\ast }$-dynamical systems. Preprint, 2017, arXiv:1712.10133]. We show that the Powers’ averaging property holds for the reduced crossed product $\unicode[STIX]{x1D6E4}\ltimes _{r}{\mathcal{A}}$ for any action $\unicode[STIX]{x1D6E4}\curvearrowright {\mathcal{A}}$ of a $C^{\ast }$-simple group $\unicode[STIX]{x1D6E4}$ on a unital $C^{\ast }$-algebra ${\mathcal{A}}$, and use it to prove a one-to-one correspondence between stationary states on ${\mathcal{A}}$ and those on $\unicode[STIX]{x1D6E4}\ltimes _{r}{\mathcal{A}}$.

scholarly journals Gauss extensions and total graded subrings for crossed product algebras

2007 ◽  
Vol 316 (1) ◽  
pp. 189-205 ◽  
Author(s):  
H.H. Brungs ◽  
H. Marubayashi ◽  
E. Osmanagic
Keyword(s):  
Crossed Product ◽  
Crossed Product Algebras
Sign in / Sign up

Export Citation Format

Share Document