scholarly journals Equivariant map superalgebras

2014 ◽  
Vol 277 (1-2) ◽  
pp. 373-399 ◽  
Author(s):  
Alistair Savage
Keyword(s):  
Equivariant Map

scholarly journals Hyperconvex representations and exponential growth

2013 ◽  
Vol 34 (3) ◽  
pp. 986-1010 ◽  
Author(s):  
A. SAMBARINO
Keyword(s):  
Symmetric Space ◽  
Fundamental Group ◽  
Lie Group ◽  
Exponential Growth ◽  
Transversality Condition ◽  
Indicator Function ◽  
Equivariant Map ◽  
Negatively Curved ◽  
Funct Anal ◽  
Growth Indicator

AbstractLet $G$ be a real algebraic semi-simple Lie group and $\Gamma $ be the fundamental group of a closed negatively curved manifold. In this article we study the limit cone, introduced by Benoist [Propriétés asymptotiques des groupes linéaires. Geom. Funct. Anal. 7(1) (1997), 1–47], and the growth indicator function, introduced by Quint [Divergence exponentielle des sous-groupes discrets en rang supérieur. Comment. Math. Helv. 77 (2002), 503–608], for a class of representations $\rho : \Gamma \rightarrow G$ admitting an equivariant map from $\partial \Gamma $ to the Furstenberg boundary of the symmetric space of $G, $ together with a transversality condition. We then study how these objects vary with the representation.

scholarly journals Equivariant Map Queer Lie Superalgebras

2016 ◽  
Vol 68 (2) ◽  
pp. 258-279 ◽  
Author(s):  
Lucas Calixto ◽  
Adriano Moura ◽  
Alistair Savage
Keyword(s):  
Finite Group ◽  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
Equivariant Map ◽  
Isomorphism Classes ◽  
Finite Dimensional ◽  
Regular Maps ◽  
A Finite Group ◽  
Special Case

AbstractAn equivariant map queer Lie superalgebra is the Lie superalgebra of regular maps from an algebraic variety (or scheme) X to a queer Lie superalgebra q that are equivariant with respect to the action of a finite group Γ acting on X and q. In this paper, we classify all irreducible finite-dimensional representations of the equivariant map queer Lie superalgebras under the assumption that Γ is abelian and acts freely on X. We show that such representations are parameterized by a certain set of Γ-equivariant finitely supported maps from X to the set of isomorphism classes of irreducible finite-dimensional representations of q. In the special case where X is the torus, we obtain a classification of the irreducible finite-dimensional representations of the twisted loop queer superalgebra.

scholarly journals Local Weyl modules for equivariant map algebras with free abelian group actions

2012 ◽  
Vol 350 (1) ◽  
pp. 386-404 ◽  
Author(s):  
Ghislain Fourier ◽  
Tanusree Khandai ◽  
Deniz Kus ◽  
Alistair Savage
Keyword(s):  
Abelian Group ◽  
Free Abelian Group ◽  
Group Actions ◽  
Weyl Modules ◽  
Equivariant Map ◽  
Abelian Group Actions

General Properties of Equivariant Cohomology

2020 ◽  
pp. 69-76
Author(s):  
Loring W. Tu
Keyword(s):  
Topological Group ◽  
Equivariant Cohomology ◽  
Disjoint Union ◽  
Ring Homomorphism ◽  
Equivariant Map ◽  
General Properties ◽  
Coefficient Ring

This chapter assesses the general properties of equivariant cohomology. Both the homotopy quotient and equivariant cohomology are functorial constructions. Equivariant cohomology is particularly simple when the action is free. Throughout the chapter, by a G-space, it means a left G-space. Let G be a topological group and consider the category of G-spaces and G-maps. A morphism of left G-spaces is a G-equivariant map (or G-map). Such a morphism induces a map of homotopy quotients. The map in turn induces a ring homomorphism in cohomology. The chapter then looks at the coefficient ring of equivariant cohomology, as well as the equivariant cohomology of a disjoint union.

scholarly journals On the action of the unitary group on the projective plane over a local field

1997 ◽  
Vol 62 (3) ◽  
pp. 371-397 ◽  
Author(s):  
Harm Voskuil
Keyword(s):  
Projective Plane ◽  
Local Field ◽  
Unitary Group ◽  
Residue Field ◽  
Equivariant Map ◽  
Rank One ◽  
Characteristic 2 ◽  
Set Of Points ◽  
Stable Points ◽  
Split Torus

AbstractLet G be a unitary group of rank one over a non-archimedean local field K (whose residue field has a characteristic ≠ 2). We consider the action of G on the projective plane. A G(K) equivariant map from the set of points in the projective plane that are semistable for every maximal K split torus in G to the set of convex subsets of the building of G(K) is constructed. This map gives rise to an equivariant map from the set of points that are stable for every maximal K split torus to the building. Using these maps one describes a G(K) invariant pure affinoid covering of the set of stable points. The reduction of the affinoid covering is given.

Geometric Pseudospectral Method on Lie Group with Application to 3D Pendulum

2013 ◽  
Vol 756-759 ◽  
pp. 3021-3029
Author(s):  
Jie Li ◽  
Hong Lei An ◽  
Xue Qiang Gu ◽  
Hong Tao Xue
Keyword(s):  
Differential Equation ◽  
Rigid Body ◽  
Lie Algebra ◽  
Lie Group ◽  
Structural Characteristics ◽  
Pseudospectral Method ◽  
Rigid Body Dynamics ◽  
Equivariant Map ◽  
Body Dynamics

General pseudospectral method is extended to Lie group by virtue of equivariant map for solving rigid dynamics on Lie group. In particular, for the problem of structural characteristics of the dynamics system can not be conserved by using general pseudospectral method directly on Lie group, the differential equation evolving on the Lie group is transformed to an equivalent differential equation evolving on a Lie algebra on which general pseudospectral method is used, so that the numerical flow of rigid body dynamics is ensured to stay on Lie group. Furthermore, structural conservativeness and numerical stabilities of this method are validated and analyzed by simulation on a 3D pendulum in comparison with using pseudospectral method directly on Lie group.

Infinite determinacy of equivariant map-germs

1985 ◽  
Vol 272 (1) ◽  
pp. 67-82 ◽  
Author(s):  
C. T. C. Wall
Keyword(s):  
Equivariant Map
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