相关论文: Pseudogroups via pseudoactions: Unifying local, gl…

Let $\mathcal G$ be a Lie supergroup with Lie superalgebra $\mathfrak g$, $\mathcal M$ a supermanifold and $\mathrm{Vec}(\mathcal M)$ the set of vector fields on $\mathcal M$. Let $\lambda:\mathfrak g\rightarrow \mathrm{Vec}(\mathcal M)$ be…

A Lie groupoid can be thought of as a generalization of a Lie group in which the multiplication is only defined for certain pairs of elements. From another perspective, Lie groupoids can be regarded as manifolds endowed with a type of…

In this paper we generalize some results of Richard Palais to the case of Lie supergroups and Lie superalgebras. More precisely, let $G$ be a Lie supergroup, $\mathfrak g$ its Lie superalgebra and let $\rho$ be an infinitesimal action (a…

The expansion method of Lie algebras by a semigroup or S-expansion is generalized to act directly on the group manifold, and not only at the level of its Lie algebra. The consistency of this generalization with the dual formulation of the…

We give a unified description of morphisms and comorphisms of Lie pseudoalgebras, showing that the both types of morphisms can be regarded as subalgebras of a Lie pseudoalgebra, called the $\psi$-sum. We also provide similar descriptions…

A particularly easy, even if for long overlooked way is presented for defining globally arbitrary Lie group actions on smooth functions on Euclidean domains. This way is based on the appropriate use of the usual parametric representation of…

Using the Lie derivative of the metric we define a class of Lie algebras of vector fields by generalising the concept of Killing vectors. As a Lie algebra they define locally a group action on the pseudo-Riemannian manifold through…

In this article we define the twisted product of groups as the generalization of the semidirect product of groups. We will find the necessary and sufficient condition in order that the twisted product of groups to be a group. In particular,…

Let X be a normal variety endowed with an algebraic torus action. An additive group action $\alpha$ on X is called vertical if a general orbit of $\alpha$ is contained in the closure of an orbit of the torus action and the image of the…

We extend the concept of a partial group action to non-associative algebras in a variety \(\mathcal{V}(I)\), solve the globalization problem within \(\mathcal{V}(I)\) and examine its universal property. It is achieved using what we call the…

A multiplicatively closed, horizontal $n$-plane field $D$ on a Lie groupoid $G$ over $M$ generalizes to intransitive geometry the classical notion of a Cartan connection. The infinitesimalization of the connection $D$ is a Cartan connection…

A generalized pseudo effect algebra (GPEA) is a partially ordered partial algebraic structure with a smallest element 0, but not necessarily with a unit (i.e, a largest element). If a GPEA admits a so-called unitizing automorphism, then it…

Questions of the following sort are addressed: Does a given Lie group or Lie algebra act effectively on a given manifold? How smooth can such actions be? What fxed-point sets are possible? What happens under perturbations? Old results are…

Lie algebras endowed with an action by automorphisms of any of the symmetric groups S3 or S4 are considered, and their decomposition into a direct sum of irreducible modules for the given action is studied. In case of S3-symmetry, the Lie…

We prove that every partial action of an inverse semigroupoid on a set admits a universal globalization. Moreover, we show that our construction gives a reflector from the category of partial actions on the full subcategory of global…

For a finite dimensional Lie algebra $\g$ of vector fields on a manifold $M$ we show that $M$ can be completed to a $G$-space in a unversal way, which however is neither Hausdorff nor $T_1$ in general. Here $G$ is a connected Lie group with…

This is an expository article on properties of actions on Lie groups by subgroups of their automorphism groups. After recalling various results on the structure of the automorphism groups, we discuss actions with dense orbits, invariant and…

Weil prolongations of a Lie group are naturally Lie groups. It is not known in the theory of infinite-dimensional Lie groups how to construct a Lie group with a given Lie algebra as its Lie algebra or whether there exists such a Lie group…

We describe explicitly Lie superalgebra isomorphisms between the Lie superalgebras of first-order superdifferential operators on supermanifolds, showing in particular that any such isomorphism induces a diffeomorphism of the supermanifolds.…

Many compactly generated pseudo-groups of local transformations on 1-manifolds are realizable as the transverse dynamic of a foliation of codimension 1 on a compact manifold of dimension 3 or 4.