scholarly journals Group actions, orbit spaces, and noncommutative deformation theory

2010 ◽  
Vol 59 (4) ◽  
pp. 364
Author(s):  
A Siqveland
Keyword(s):  
Deformation Theory ◽  
Group Actions ◽  
Orbit Spaces

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.

On orbit spaces of compact group actions

1982 ◽  
Vol 40 (3-4) ◽  
pp. 209-215
Author(s):  
Satya Deo ◽  
P. Palanichamy
Keyword(s):  
Compact Group ◽  
Group Actions ◽  
Orbit Spaces

scholarly journals Equivariant one-parameter formal deformations of Hom-Leibniz algebras

2020 ◽  
pp. 2050082
Author(s):  
Goutam Mukherjee ◽  
Ripan Saha
Keyword(s):  
Finite Group ◽  
Deformation Theory ◽  
Group Actions ◽  
Finite Group Actions ◽  
Leibniz Algebras ◽  
New Type

The aim of this paper is to define a new type of cohomology for multiplicative Hom-Leibniz algebras which control deformations of Hom-Leibniz algebras. The cohomology and the associated deformation theory for Hom-Leibniz algebras as developed here are also extended to equivariant context, under the presence of finite group actions on Hom-Leibniz algebras.

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