scholarly journals Local rigidity of certain solvable group actions on tori

2021 ◽  
Vol 41 (2) ◽  
pp. 553-567
Author(s):  
Qiao Liu ◽  
Keyword(s):  
Solvable Group ◽  
Group Actions ◽  
Local Rigidity

scholarly journals Topological transitivity of solvable group actions on the line R

2009 ◽  
Vol 116 (2) ◽  
pp. 203-215 ◽  
Author(s):  
Suhua Wang ◽  
Enhui Shi ◽  
Lizhen Zhou ◽  
Grant Cairns
Keyword(s):  
Solvable Group ◽  
Group Actions ◽  
Topological Transitivity

scholarly journals Measure rigidity for solvable group actions in the space of lattices

2019 ◽  
Vol 189 (3) ◽  
pp. 421-428
Author(s):  
Manfred Einsiedler ◽  
Ronggang Shi
Keyword(s):  
Solvable Group ◽  
Group Actions ◽  
Measure Rigidity

Local rigidity problem of smooth group actions

2017 ◽  
Vol 30 (2) ◽  
pp. 207-233
Author(s):  
Masayuki Asaoka
Keyword(s):  
Group Actions ◽  
Local Rigidity ◽  
Smooth Group Actions

Group actions and non-vanishing elements in solvable groups

2020 ◽  
Vol 23 (6) ◽  
pp. 1103-1109
Author(s):  
Thomas R. Wolf
Keyword(s):  
Solvable Group ◽  
Group Actions ◽  
Solvable Groups ◽  
Direct Sum ◽  
Irreducible Modules ◽  
Group A ◽  
Vanishing Elements

AbstractFor a solvable group, a theorem of Gaschutz shows that {F(G)/\Phi(G)} is a direct sum of irreducible G-modules and a faithful {G/F(G)}-module. If each of these irreducible modules is primitive, we show that every non-vanishing element of G lies in {F(G)}.

scholarly journals Global rigidity of solvable group actions onS1

2004 ◽  
Vol 8 (2) ◽  
pp. 877-924 ◽  
Author(s):  
Lizzie Burslem ◽  
Amie Wilkinson
Keyword(s):  
Solvable Group ◽  
Group Actions ◽  
Global Rigidity

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.

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