scholarly journals Injectivity, crossed products, and amenable group actions

2020 ◽  
pp. 105-137
Author(s):  
Alcides Buss ◽  
Siegfried Echterhoff ◽  
Rufus Willett
Keyword(s):  
Amenable Group ◽  
Group Actions ◽  
Crossed Products

scholarly journals The Katok's entropy formula for amenable group actions

2018 ◽  
Vol 38 (9) ◽  
pp. 4467-4482
Author(s):  
Xiaojun Huang ◽  
◽  
Jinsong Liu ◽  
Changrong Zhu ◽  
◽  
...  
Keyword(s):  
Amenable Group ◽  
Group Actions ◽  
Entropy Formula

scholarly journals Zero-dimensional extensions of amenable group actions

2021 ◽  
Vol 256 (2) ◽  
pp. 121-145
Author(s):  
Dawid Huczek
Keyword(s):  
Amenable Group ◽  
Group Actions

scholarly journals Almost Finiteness for General Étale Groupoids and Its Applications to Stable Rank of Crossed Products

2018 ◽  
Vol 2020 (19) ◽  
pp. 6007-6041 ◽  
Author(s):  
Yuhei Suzuki
Keyword(s):  
Amenable Group ◽  
Cantor Set ◽  
Stable Rank ◽  
Crossed Product ◽  
Local Version ◽  
Crossed Products ◽  
Subexponential Growth ◽  
Minimal Action ◽  
New Strategy ◽  
Totally Disconnected

Abstract We extend Matui’s notion of almost finiteness to general étale groupoids and show that the reduced groupoid C$^{\ast }$-algebras of minimal almost finite groupoids have stable rank 1. The proof follows a new strategy, which can be regarded as a local version of the large subalgebra argument. The following three are the main consequences of our result: (1) for any group of (local) subexponential growth and for any its minimal action admitting a totally disconnected free factor, the crossed product has stable rank 1; (2) any countable amenable group admits a minimal action on the Cantor set, all whose minimal extensions form the crossed product of stable rank 1; and (3) for any amenable group, the crossed product of the universal minimal action has stable rank 1.

Relative Entropy and Mean Li–Yorke Chaos for Biorderable Amenable Group Actions

2020 ◽  
Vol 30 (02) ◽  
pp. 2050032
Author(s):  
Kesong Yan ◽  
Fanping Zeng
Keyword(s):  
Topological Entropy ◽  
Relative Entropy ◽  
Amenable Group ◽  
Group Actions

We consider the relative entropy and mean Li–Yorke chaos for [Formula: see text]-systems, where [Formula: see text] is a countable discrete infinite biorderable amenable group. We prove that positive relative topological entropy implies a multivariant version of mean Li–Yorke chaos on fibers for a [Formula: see text]-system.

scholarly journals Periodic points for amenable group actions on uniquely arcwise connected continua

2020 ◽  
pp. 1-12
Author(s):  
ENHUI SHI ◽  
XIANGDONG YE
Keyword(s):  
Periodic Point ◽  
Amenable Group ◽  
Group Actions ◽  
Periodic Points ◽  
Arcwise Connected

Abstract We show that any action of a countable amenable group on a uniquely arcwise connected continuum has a periodic point of order $\leq 2$ .

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