共查询到19条相似文献,搜索用时 46 毫秒
1.
在这篇文章中,我们讨论了李双代数胚之间的态射,得到了一些李双代数胚之间态射的性质.研究了泊松群胚在泊松流形上的泊松作用,以及这个泊松作用与被作用流形的切李双代数胚到作用泊松群胚的切李双代数胚之间的态射的关系,得到了一些有用的结论。 相似文献
2.
定义了纤维丛的相配群胚的概念,从作用的角度研究了李群胚与主丛的关系;给出了一个泊松群胚在泊松流形上的作用是泊松作用的充要条件;文末得到了一些关于泊松流形上Casimir函数的结果. 相似文献
3.
孟道骥等对完备李代数作了系统的研究并已获得很多基本和重要的结果。本文给出完备李群与完备李代数的某些关系。 相似文献
4.
5.
6.
7.
8.
《数学的实践与认识》2013,(20)
研究了辛群胚与泊松群胚的作用.利用李群胚作用及相关性质,得到了李群胚作用成为辛群胚和泊松群胚作用的充要条件,推广了辛群胚和泊松群胚的性质,为辛群胚与泊松群胚理论的进一步研究起到了推动作用. 相似文献
9.
10.
本文证明了任何半单李代数(或者李群)在连通光滑流形上的非平凡单纯作用一定没有驻点.而且有效作用的那部分必定是同构于sl(2,R)(或者SL(2,R))的理想. 相似文献
11.
Stéphane Vassout 《Journal of Functional Analysis》2006,236(1):161-200
We develop an abstract theory of unbounded longitudinal pseudodifferential calculus on smooth groupoids (also called Lie groupoids) with compact basis. We analyze these operators as unbounded operators acting on Hilbert modules over C∗(G), and we show in particular that elliptic operators are regular. We construct a scale of Sobolev modules which are the abstract analogues of the ordinary Sobolev spaces, and analyze their properties. Furthermore, we show that complex powers of positive elliptic pseudodifferential operators are still pseudodifferential operators in a generalized sense. 相似文献
12.
Let K be a Lie group and P be a K-principal bundle on a manifold M. Suppose given furthermore a central extension of K. It is a classical question whether there exists a -principal bundle on M such that . Neeb (Commun. Algebra 34:991–1041, 2006) defines in this context a crossed module of topological Lie algebras whose cohomology
class is an obstruction to the existence of . In the present article, we show that is up to torsion a full obstruction for this problem, and we clarify its relation to crossed modules of Lie algebroids and
Lie groupoids, and finally to gerbes.
相似文献
13.
We prove a general integrability result for matched pairs of Lie algebroids. (Matched pairs of Lie algebras are also known as double Lie algebras or twilled extensions of Lie algebras.) The method used is an extension of a method introduced by Lu and Weinstein in the case of Poisson Lie groups, and yields double groupoids which satisfy an étale form of the vacancy condition. 相似文献
14.
《Indagationes Mathematicae》2014,25(5):1019-1053
15.
David Iglesias Juan C. Marrero David Martín de Diego Eduardo Martínez 《Journal of Nonlinear Science》2008,18(3):221-276
This paper studies the construction of geometric integrators for nonholonomic systems. We develop a formalism for nonholonomic
discrete Euler–Lagrange equations in a setting that permits to deduce geometric integrators for continuous nonholonomic systems
(reduced or not). The formalism is given in terms of Lie groupoids, specifying a discrete Lagrangian and a constraint submanifold
on it. Additionally, it is necessary to fix a vector subbundle of the Lie algebroid associated to the Lie groupoid. We also
discuss the existence of nonholonomic evolution operators in terms of the discrete nonholonomic Legendre transformations and
in terms of adequate decompositions of the prolongation of the Lie groupoid. The characterization of the reversibility of
the evolution operator and the discrete nonholonomic momentum equation are also considered. Finally, we illustrate with several
classical examples the wide range of application of the theory (the discrete nonholonomic constrained particle, the Suslov
system, the Chaplygin sleigh, the Veselova system, the rolling ball on a rotating table and the two wheeled planar mobile
robot).
This work was partially supported by MEC (Spain) Grants MTM 2006-03322, MTM 2007-62478, MTM 2006-10531, project “Ingenio Mathematica”
(i-MATH) No. CSD 2006-00032 (Consolider-Ingenio 2010) and S-0505/ESP/0158 of the CAM. 相似文献
16.
17.
We define the “localized index” of longitudinal elliptic operators on Lie groupoids associated with Lie algebroid cohomology classes. We derive a topological expression for these numbers using the algebraic index theorem for Poisson manifolds on the dual of the Lie algebroid. Underlying the definition and computation of the localized index, is an action of the Hopf algebroid of jets around the unit space, and the characteristic map it induces on Lie algebroid cohomology. This map can be globalized to differentiable groupoid cohomology, giving a definition of the “global index”, that can be computed by localization. This correspondence between the “global” and “localized” index is given by the van Est map for Lie groupoids. 相似文献
18.
《Mathematische Nachrichten》2018,291(13):1989-2007
Given a basic closed 1‐form on a Lie groupoid , the Morse–Novikov cohomology groups are defined in this paper. They coincide with the usual de Rham cohomology groups when θ is exact and with the usual Morse–Novikov cohomology groups when is the unit groupoid generated by a smooth manifold M. We prove that the Morse–Novikov cohomology groups are invariant under Morita equivalences of Lie groupoids. On orbifold groupoids, we show that these groups are isomorphic to sheaf cohomology groups. Finally, when θ is not exact, we extend a vanishing theorem from smooth manifolds to orbifold groupoids. 相似文献
19.
I. Moerdijk 《K-Theory》2003,28(3):207-258
We observe that any regular Lie groupoid G over a manifold M fits into an extension K G E of a foliation groupoid E by a bundle of connected Lie groups K. If F is the foliation on M given by the orbits of E and T is a complete transversal to F , this extension restricts to T, as an extension K
T
G
T
E
T
of an étale groupoid E
T
by a bundle of connected groups K
T
. We break up the classification problem for regular Lie groupoids into two parts. On the one hand, we classify the latter extensions of étale groupoids by (non-Abelian) cohomology classes in a new ech cohomology of étale groupoids. On the other hand, given K and E and an extension K
T
G
T
E
T
over T, we present a cohomological obstruction to the problem of whether this is the restriction of an extension K G E over M; if this obstruction vanishes, all extensions K G E over M which restrict to a given extension over the transversal together form a principal bundle over a group of bitorsors under K. 相似文献