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Infinite Group Actions on Polyhedra
In the past fifteen years, the theory of right-angled Artin groups and special cube complexes has emerged as a central topic in geometric group...
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Group Actions
We outline group action and substantiate with various examples. Group action is a potent tool which can be employed to gain insight into the...
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On Hom-groups and Hom-group Actions
A Hom-group is the non-associative generalization of a group whose associativity and unitality are twisted by a compatible bijective map. In this...
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Rokhlin-Type Properties of Group Actions on Operator Algebras
We give a survey of Rokhlin-type properties of group actions on operator algebras. Though we briefly review the classification of group actions on...
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Compact Group Actions and Boundaries
Geometric group theory is devoted to the interplay between the algebraic structure of a group and properties of its actions on geometric and...
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A Spectral Sequence for Locally Free Isometric Lie Group Actions
We present a spectral sequence for free isometric Lie algebra actions (and consequently locally free isometric Lie group actions) which relates the...
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Expansive Lie Group Actions
In this work, we introduce a concept of expansiveness for actions of connected Lie groups. We study some of its properties and investigate some...
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Intrinsic Ergodicity, Generators, and Symbolic Representations of Algebraic Group Actions
AbstractWe construct natural symbolic representations of intrinsically ergodic, but not necessarily expansive, principal algebraic actions of...
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Almost Periodic Type Group Actions on Compact Quantum Metric Spaces
A compact quantum metric space is a complete order unit space A endowed with a Lipnorm L . We give some characterizations of almost periodic type...
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Polynomial Entropy of Amenable Group Actions for Noncompact Sets
In this paper, we define and study polynomial entropy on an arbitrary subset and local measure theoretic polynomial entropy for any Borel probability...
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Group Actions on Twisted Sums of Banach Spaces
We study bounded actions of groups and semigroups G on exact sequences of Banach spaces from the point of view of (generalized) quasilinear maps,...
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Rationality Problem of Two-Dimensional Quasi-Monomial Group Actions
The rationality problem of two-dimensional purely quasi-monomial actions was solved completely by (Hoshi, Kang and Kitayama, J. Algebra 403 , 363-400,
2014... -
Invariants of Finite and Discrete Group Actions via Moving Frames
A new, elementary algorithm for constructing complete, minimal sets of generating invariants for finite or, more generally, discrete group actions,...
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On the Topological Entropy of Saturated Sets for Amenable Group Actions
Let ( X , G ) be a G -action topological system, where G is a countable infinite discrete amenable group and X a compact metric space. We prove a...
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Isometric Lie 2-Group Actions on Riemannian Groupoids
We study isometric actions of Lie 2-groups on Riemannian groupoids by exhibiting some of their immediate properties and implications. Firstly, we...
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A Note on the Entropy for Heisenberg Group Actions on the Torus
In this paper, the entropy of discrete Heisenberg group actions is considered. Let α be a discrete Heisenberg group action on a compact metric space X. ...
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The pressure of intricacy and average sample complexity for amenable group actions
Let ( X , G ) be a G -system, where G is an infinite countable discrete amenable group and X is a compact metric space with a metric d . In this paper, we...
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Curvatures and Austere Property of Orbits of Path Group Actions Induced by Hermann Actions
It is known that an isometric action of a Lie group on a compact symmetric space gives rise to a proper Fredholm action of a path group on a path...
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Classification of momentum proper exact Hamiltonian group actions and the equivariant Eliashberg cotangent bundle conjecture
Let G be a compact and connected Lie group. The Hamiltonian G -model functor maps the category of symplectic representations of closed subgroups of G ...
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Equicontinuity and Sensitivity of Group Actions
Let ( X, G ) be a dynamical system ( G -system for short), that is, X is a topological space and G is an infinite topological group continuously acting...