Cohomology and the absence of strong ergodicity for ergodic group actions

1985 ◽  
pp. 486-496 ◽  
Author(s):  
Klaus Schmidt
Keyword(s):  
Group Actions ◽  
Strong Ergodicity

scholarly journals Amenability, Kazhdan's property T, strong ergodicity and invariant means for ergodic group-actions

1981 ◽  
Vol 1 (2) ◽  
pp. 223-236 ◽  
Author(s):  
Klaus Schmidt
Keyword(s):  
Group Action ◽  
Measure Space ◽  
Group Actions ◽  
Finite Measure ◽  
Countable Group ◽  
Invariant Sets ◽  
Amenable Groups ◽  
Strong Ergodicity ◽  
Property T ◽  
Invariant Means

AbstractThis paper discusses the relations between the following properties o finite measure preserving ergodic actions of a countable group G: strong ergodicity (i.e. the non-existence of almost invariant sets), uniqueness of G-invariant means on the measure space carrying the group action, and certain cohomological properties. Using these properties one can characterize all actions of amenable groups and of groups with Kazhdan's property T. For groups which fall in between these two definations these notions lead to some interesting examples.

Generating pairs and group actions

2014 ◽  
Vol 218 (5) ◽  
pp. 777-783
Author(s):  
Darryl McCullough
Keyword(s):  
Group Actions

scholarly journals The close relation between border and Pommaret marked bases

2021 ◽  
Author(s):  
Cristina Bertone ◽  
Francesca Cioffi
Keyword(s):  
Finite Order ◽  
Polynomial Ring ◽  
Group Actions ◽  
Close Relation ◽  
Open Covering ◽  
Order Ideal ◽  
Lower Dimension ◽  
Hilbert Schemes ◽  
Affine Spaces ◽  
The Ideal

AbstractGiven a finite order ideal $${\mathcal {O}}$$ O in the polynomial ring $$K[x_1,\ldots , x_n]$$ K [ x 1 , … , x n ] over a field K, let $$\partial {\mathcal {O}}$$ ∂ O be the border of $${\mathcal {O}}$$ O and $${\mathcal {P}}_{\mathcal {O}}$$ P O the Pommaret basis of the ideal generated by the terms outside $${\mathcal {O}}$$ O . In the framework of reduction structures introduced by Ceria, Mora, Roggero in 2019, we investigate relations among $$\partial {\mathcal {O}}$$ ∂ O -marked sets (resp. bases) and $${\mathcal {P}}_{\mathcal {O}}$$ P O -marked sets (resp. bases). We prove that a $$\partial {\mathcal {O}}$$ ∂ O -marked set B is a marked basis if and only if the $${\mathcal {P}}_{\mathcal {O}}$$ P O -marked set P contained in B is a marked basis and generates the same ideal as B. Using a functorial description of these marked bases, as a byproduct we obtain that the affine schemes respectively parameterizing $$\partial {\mathcal {O}}$$ ∂ O -marked bases and $${\mathcal {P}}_{\mathcal {O}}$$ P O -marked bases are isomorphic. We are able to describe this isomorphism as a projection that can be explicitly constructed without the use of Gröbner elimination techniques. In particular, we obtain a straightforward embedding of border schemes in affine spaces of lower dimension. Furthermore, we observe that Pommaret marked schemes give an open covering of Hilbert schemes parameterizing 0-dimensional schemes without any group actions. Several examples are given throughout the paper.

scholarly journals Schottky groups acting on homogeneous rational manifolds

2019 ◽  
Vol 2019 (753) ◽  
pp. 23-56 ◽  
Author(s):  
Christian Miebach ◽  
Karl Oeljeklaus
Keyword(s):  
Deformation Theory ◽  
Group Actions ◽  
Picard Group ◽  
Schottky Group ◽  
Fundamental Groups ◽  
Complex Manifolds ◽  
Schottky Groups ◽  
Algebraic Dimension ◽  
Geometric Invariants ◽  
Compact Complex Manifolds

AbstractWe systematically study Schottky group actions on homogeneous rational manifolds and find two new families besides those given by Nori’s well-known construction. This yields new examples of non-Kähler compact complex manifolds having free fundamental groups. We then investigate their analytic and geometric invariants such as the Kodaira and algebraic dimension, the Picard group and the deformation theory, thus extending results due to Lárusson and to Seade and Verjovsky. As a byproduct, we see that the Schottky construction allows to recover examples of equivariant compactifications of {{\rm{SL}}(2,\mathbb{C})/\Gamma} for Γ a discrete free loxodromic subgroup of {{\rm{SL}}(2,\mathbb{C})}, previously obtained by A. Guillot.

Modeling the Genetic Algorithm by a Nonhomogeneous Markov Chain: Weak and Strong Ergodicity

2013 ◽  
Vol 57 (1) ◽  
pp. 144-151 ◽  
Author(s):  
V. S. M. Campos ◽  
A. G. C. Pereira ◽  
J. A. Rojas Cruz
Keyword(s):  
Genetic Algorithm ◽  
Markov Chain ◽  
Strong Ergodicity ◽  
Nonhomogeneous Markov Chain

scholarly journals Lifting group actions and nonnegative curvature

2011 ◽  
Vol 363 (06) ◽  
pp. 2865-2865 ◽  
Author(s):  
Karsten Grove ◽  
Wolfgang Ziller
Keyword(s):  
Group Actions ◽  
Nonnegative Curvature

Supersingularity from group actions

2008 ◽  
Vol 281 (4) ◽  
pp. 575-581
Author(s):  
Riccardo Re
Keyword(s):  
Group Actions
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