Related papers: Generalized Group Actions in a Global Setting
The description of invariants of surfaces with respect to the motion groups is reduced to the description of invariants of parameterized surfaces with respect to the motion groups. Existence of a commuting system of invariant partial…
A simple pedagogical introduction to the Colombeau algebra of generalised functions is presented, leading the standard definition.
We use the combinatorial harmonic map theory to study the isometric actions of discrete groups on Hadamard spaces. Given a finitely generated group acting by automorphisms, properly discontinuously and cofinitely on a simplicial complex and…
We use spectral theory to produce embeddings of distributions in the algebras of generalized functions on a closed Riemannian manifold. These embeddings are invariant under isometries and preserve the singularity structure of the…
We derive the group structure for cyclotomic function fields obtained by applying the Carlitz action for extensions of an initial constant field. The tame and wild structures are isolated to describe the Galois action on differentials. We…
In a series of papers we proposed a model unifying general relativity and quantum mechanics. The idea was to deduce both general relativity and quantum mechanics from a noncommutative algebra ${\cal A}_{\Gamma}$ defined on a transformation…
In this paper we study the notion of configuration for group actions. It is proved that some properties concerning configuration of groups can be extended for the case of group actions. The relationship between configuration and different…
Generalized planning is concerned with the computation of plans that solve not one but multiple instances of a planning domain. Recently, it has been shown that generalized plans can be expressed as mappings of feature values into actions,…
The Colombeau algebra of generalized functions allows to unrestrictedly carry out products of distributions. We analyze this operation from a microlocal point of view, deriving a general inclusion relation for wave front sets of products in…
Let $M_1$ and $M_2$ be two $n$-dimensional smooth manifolds with boundary. Suppose we glue $M_1$ and $M_2$ along some boundary components (which are, therefore, diffeomorphic). Call the result $N.$ If we have a group $G$ acting continuously…
We adapt a nonlinear version of Peetre's theorem on local operators in order to investigate representatives of nonlinear generalized functions occurring in the theory of full Colombeau algebras.
If $G$ is a compact group acting continuously on a compact metric space $(X, m)$, we prove two results that generalize Dirichlet's classical theorem on Diophantine approximation. If $G$ is a noncommutative compact group of isometries, we…
We present a geometric approach to diffeomorphism invariant full Colombeau algebras which allows a particularly clear view on the construction of the intrinsically defined algebra $\hat{\mathcal G}(M)$ on the manifold $M$ given in (Grosser…
We use tools from combinatorial group theory in order to study actions of three types on groups acting on a curve, namely the automorphism group of a compact Riemann surface, the mapping class group acting on a surface (which now is allowed…
In this paper we first consider the Hamiltonian action of a compact connected Lie group on an $H$-twisted generalized complex manifold $M$. Given such an action, we define generalized equivariant cohomology and generalized equivariant…
This paper presents the theory of non-smooth Lie group actions on chains of Banach manifolds. The rigorous functional analytic spaces are given to deal with quotients of such actions. A hydrodynamical example is studied in detail.
We address several problems concerning the geometry of the space of Hermitian operators on a finite-dimensional Hilbert space, in particular the geometry of the space of density states and canonical group actions on it. For quantum…
We study and relate certain actions and extensions involving 2-groups.
We study finite-dimensional groups definable in models of the theory of real closed fields with a generic derivation (also known as CODF). We prove that any such group definably embeds in a semialgebraic group. We extend the results to…
In this paper we discuss generalized group, provides some interesting examples. Further we introduce a generalized module as a module like structure obtained from a generalized group and discuss some of its properties and we also describes…