Search results for "Group action"

Group Actions and Asymptotic Behavior of Graded Polynomial Identities

2002

Analytic curves in power series rings

1990

Proper triangular Ga-actions on A^4 are translations

2013

We describe the structure of geometric quotients for proper locally triangulable additve group actions on locally trivial A^3-bundles over a noetherian normal base scheme X defined over a field of characteristic 0. In the case where dim X=1, we show in particular that every such action is a translation with geometric quotient isomorphic to the total space of a vector bundle of rank 2 over X. As a consequence, every proper triangulable Ga-action on the affine four space A^4 over a field of characteristic 0 is a translation with geometric quotient isomorphic to A^3.

Archimedean actions on median pretrees

2001

In this paper we consider group actions on generalized treelike structures (termed ‘pretrees’) defined simply in terms of betweenness relations. Using a result of Levitt, we show that if a countable group admits an archimedean action on a median pretree, then it admits an action by isometries on an [open face R]-tree. Thus the theory of isometric actions on [open face R]-trees may be extended to a more general setting where it merges naturally with the theory of right-orderable groups. This approach has application also to the study of convergence group actions on continua.

Some Nonlinear Methods in Fréchet Operator Rings and Ψ*-Algebras

1995

Two different inverse function theorems, one of Nash-Moser type, the other due to H. Omori, are extended to obtain special surjectivity results in locally convex and locally pseudo-convex Frechet algebras generated by group actions and derivations. In particular, the following factorization problem is discussed. Let Ψ be a locally pseudo-convex Frechet algebra with unit e and T+ : Ψ Ψ a continuous linear operator. Does there exist a neighborhood U of 0 such that the equation where T- = IΨ- T, has a solution x ∈ Ψ for every y ∈ U?

Finding Invariants of Group Actions on Function Spaces, a General Methodology from Non-Abelian Harmonic Analysis

2008

In this paper, we describe a general method using the abstract non-Abelian Fourier transform to construct “rich” invariants of group actions on functional spaces.

Rationally integrable vector fields and rational additive group actions

2016

International audience; We characterize rational actions of the additive group on algebraic varieties defined over a field of characteristic zero in terms of a suitable integrability property of their associated velocity vector fields. This extends the classical correspondence between regular actions of the additive group on affine algebraic varieties and the so-called locally nilpotent derivations of their coordinate rings. Our results lead in particular to a complete characterization of regular additive group actions on semi-affine varieties in terms of their associated vector fields. Among other applications, we review properties of the rational counterpart of the Makar-Limanov invariant…

The varieties of bifocal Grassmann tensors

2022

AbstractGrassmann tensors arise from classical problems of scene reconstruction in computer vision. In particular, bifocal Grassmann tensors, related to a pair of projections from a projective space onto view spaces of varying dimensions, generalize the classical notion of fundamental matrices. In this paper, we study in full generality the variety of bifocal Grassmann tensors focusing on its birational geometry. To carry out this analysis, every object of multi-view geometry is described both from an algebraic and geometric point of view, e.g., the duality between the view spaces, and the space of rays is explicitly described via polarity. Next, we deal with the moduli of bifocal Grassmann…

groups acting on the line and the circle with at most N fixed points

2022

A classical theme in dynamical systems is that the first fundamental information comes from the understanding of periodic orbits. When studying group actions, this means that we want to understand the fixed points of elements of the group, and a natural question that emerges from that is: Which groups of homeomorphisms can act on a 1-manifold having all non-trivial elements with at most N fixed points? Our main objective in this work is to approach that question and understand what properties can such dynamical hypothesis induces to the group.For the case N=0, a classical result from O. Hölder implies that such group of homeomorphisms acting on the line is always semi-conjugate to a subgrou…

Hyperbolicity as an obstruction to smoothability for one-dimensional actions

2017

Ghys and Sergiescu proved in the $80$s that Thompson's group $T$, and hence $F$, admits actions by $C^{\infty}$ diffeomorphisms of the circle . They proved that the standard actions of these groups are topologically conjugate to a group of $C^\infty$ diffeomorphisms. Monod defined a family of groups of piecewise projective homeomorphisms, and Lodha-Moore defined finitely presentable groups of piecewise projective homeomorphisms. These groups are of particular interest because they are nonamenable and contain no free subgroup. In contrast to the result of Ghys-Sergiescu, we prove that the groups of Monod and Lodha-Moore are not topologically conjugate to a group of $C^1$ diffeomorphisms. Fur…