scholarly journals K-groups of the full group actions on one-sided topological Markov shifts

2013 ◽  
Vol 33 (8) ◽  
pp. 3753-3765 ◽  
Author(s):  
Kengo Matsumoto
Keyword(s):  
Group Actions ◽  
Full Group ◽  
Markov Shifts

scholarly journals Cohomology groups, continuous full groups and continuous orbit equivalence of topological Markov shifts

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Kengo Matsumoto
Keyword(s):  
Group Actions ◽  
Full Group ◽  
Orbit Equivalence ◽  
Cohomology Groups ◽  
Shift Spaces ◽  
Markov Shifts

<p style='text-indent:20px;'>We will study several subgroups of continuous full groups of one-sided topological Markov shifts from the view points of cohomology groups of full group actions on the shift spaces. We also study continuous orbit equivalence and strongly continuous orbit equivalence in terms of these subgroups of the continuous full groups and the cohomology groups.</p>

THE RATIONALITY PROBLEM FOR THREE- AND FOUR-DIMENSIONAL PERMUTATIONAL GROUP ACTIONS

2011 ◽  
Vol 21 (08) ◽  
pp. 1317-1337
Author(s):  
IVO MICHAILOV MICHAILOV
Keyword(s):  
Rational Function ◽  
Function Field ◽  
Abelian Subgroup ◽  
Abelian Groups ◽  
Group Actions ◽  
Positive Answer ◽  
Roots Of Unity ◽  
Full Group ◽  
Noether’S Problem ◽  
Rationality Problem

Assume that K is a field, containing the full group of 4th roots of unity μ4, and char K ≠2, 3. Let G be a finite non-abelian subgroup of GL n(K) for n = 3 or n = 4. The group G induces an action on K(x1,…,xn), the rational function field of n variables over K. Consider groups represented by matrices such that in each row and column there is exactly one element from μ4 and all other elements are 0. With the aid of GAP [3] we find that there are precisely 230 such non-abelian groups in SL 4(K) and 33 in GL 3(K), up to conjugacy. We show that the fixed subfield K(x1,…,xn)G is rational (i.e. purely transcendental) over K for every such group G. We also give a positive answer to the Noether's problem for several families of groups of order m = 2a ⋅ 3b, where a ≥ 2 and b = 0, 1.

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.

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
Sign in / Sign up

Export Citation Format

Share Document