Chain transitivity for semigroup actions on flag bundles

2012 ◽  
Vol 193 (3) ◽  
pp. 817-836 ◽  
Author(s):  
Josiney A. Souza
Keyword(s):  
Semigroup Actions ◽  
Chain Transitivity

Some dynamical properties for free semigroup actions

2018 ◽  
Vol 18 (04) ◽  
pp. 1850032 ◽  
Author(s):  
Huihui Hui ◽  
Dongkui Ma
Keyword(s):  
Metric Space ◽  
Free Semigroup ◽  
Semigroup Action ◽  
Compact Metric Space ◽  
Shadowing Property ◽  
Semigroup Actions ◽  
Specification Property ◽  
Chain Transitivity ◽  
Weakly Mixing ◽  
Dynamical Properties

In this paper, we introduce the notions of weakly mixing and totally transitivity for a free semigroup action. Let [Formula: see text] be a free semigroup acting on a compact metric space generated by continuous open self-maps. Assuming shadowing for [Formula: see text] we relate the average shadowing property of [Formula: see text] to totally transitivity and its variants. Also, we study some properties such as mixing, shadowing and average shadowing properties, transitivity, chain transitivity, chain mixing and specification property for a free semigroup action.

Joint continuity of affine semigroup actions

1980 ◽  
Vol 21 (1) ◽  
pp. 153-165 ◽  
Author(s):  
Dietrich Helmer
Keyword(s):  
Semigroup Actions ◽  
Joint Continuity ◽  
Affine Semigroup

Semigroup actions on ordered groupoids

2013 ◽  
Vol 63 (1) ◽  
Author(s):  
Niovi Kehayopulu ◽  
Michael Tsingelis
Keyword(s):  
Commutative Semigroup ◽  
Equivalence Relation ◽  
Semigroup Actions ◽  
Ordered Groupoid ◽  
Quasi Order

AbstractIn this paper we prove that if S is a commutative semigroup acting on an ordered groupoid G, then there exists a commutative semigroup S̃ acting on the ordered groupoid G̃:=(G × S)/ρ̄ in such a way that G is embedded in G̃. Moreover, we prove that if a commutative semigroup S acts on an ordered groupoid G, and a commutative semigroup S̄ acts on an ordered groupoid Ḡ in such a way that G is embedded in S̄, then the ordered groupoid G̃ can be also embedded in Ḡ. We denote by ρ̄ the equivalence relation on G × S which is the intersection of the quasi-order ρ (on G × S) and its inverse ρ −1.

scholarly journals Simplicity of skew inverse semigroup rings with applications to Steinberg algebras and topological dynamics

2019 ◽  
Vol 31 (3) ◽  
pp. 543-562 ◽  
Author(s):  
Viviane Beuter ◽  
Daniel Gonçalves ◽  
Johan Öinert ◽  
Danilo Royer
Keyword(s):  
Inverse Semigroup ◽  
Semigroup Ring ◽  
Topological Dynamics ◽  
Topological Properties ◽  
Semigroup Rings ◽  
Partial Action ◽  
Semigroup Actions ◽  
Formula One ◽  
Topological Inverse Semigroup ◽  
Commutative Subring

Abstract Given a partial action π of an inverse semigroup S on a ring {\mathcal{A}} , one may construct its associated skew inverse semigroup ring {\mathcal{A}\rtimes_{\pi}S} . Our main result asserts that, when {\mathcal{A}} is commutative, the ring {\mathcal{A}\rtimes_{\pi}S} is simple if, and only if, {\mathcal{A}} is a maximal commutative subring of {\mathcal{A}\rtimes_{\pi}S} and {\mathcal{A}} is S-simple. We apply this result in the context of topological inverse semigroup actions to connect simplicity of the associated skew inverse semigroup ring with topological properties of the action. Furthermore, we use our result to present a new proof of the simplicity criterion for a Steinberg algebra {A_{R}(\mathcal{G})} associated with a Hausdorff and ample groupoid {\mathcal{G}} .

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