Results 51 to 60 of about 2,128,372 (188)
From Lie Algebras to Lie Groups within Synthetic Differential Geometry:Weil Sprouts of Lie's Third Fundamental Theorem [PDF]
arXiv, 2013 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 at all. We will show in this paper how to construct some Weil prolongations of this mythical Lie group from a given
arxiv
Cohomologies of difference Lie groups and van Est theorem [PDF]
J. Algebra 645 (2024), 116-142, 2022 A difference Lie group is a Lie group equipped with a difference operator, equivalently a crossed homomorphism with respect to the adjoint action. In this paper, first we introduce the notion of a representation of a difference Lie group, and establish the relation between representations of difference Lie groups and representations of difference Lie ...
arxiv
An introduction to Lie group integrators -- basics, new developments and applications
, 2012 We give a short and elementary introduction to Lie group methods. A selection of applications of Lie group integrators are discussed. Finally, a family of symplectic integrators on cotangent bundles of Lie groups is presented and the notion of discrete ...
Blanes +70 more
core +1 more source
Reduction of Symplectic Lie Algebroids by a Lie Subalgebroid and a Symmetry Lie Group
Symmetry, Integrability and Geometry: Methods and Applications, 2007 We describe the reduction procedure for a symplectic Lie algebroid by a Lie subalgebroid and a symmetry Lie group. Moreover, given an invariant Hamiltonian function we obtain the corresponding reduced Hamiltonian dynamics. Several examples illustrate the
David Iglesias +4 more
doaj
Soft shape registration under Lie group frame
IET Computer Vision, 2013 In this study, the authors address a two‐dimensional (2D) shape registration problem on data with anisotropic‐scale deformation and noise. First, the model is formulated under the iterative closest point (ICP) framework, which is one of the most popular ...
Yaxin Peng +3 more
doaj +1 more source
Towards a Lie theory for locally convex groups [PDF]
Japanese Journal of Math. 1 (2006), 291-468, 2015 In this survey, we report on the state of the art of some of the fundamental problems in the Lie theory of Lie groups modeled on locally convex spaces, such as integrability of Lie algebras, integrability of Lie subalgebras to Lie subgroups, and integrability of Lie algebra extensions to Lie group extensions. We further describe how regularity or local
arxiv
Hamiltonian dynamics on matched pairs
, 2016 It is shown that the cotangent bundle of a matched pair Lie group is itself a matched pair Lie group. The trivialization of the cotangent bundle of a matched pair Lie group are presented.
Esen, Oğul, Sütlü, Serkan
core +1 more source
AIMS MathematicsIn this paper, we consider the symmetry algebra of the geodesic equations of the canonical connection on a Lie group. We mainly consider the solvable indecomposable six-dimensional Lie algebras with co-dimension two abelian nilradical that have an ...
Nouf Almutiben +3 more
doaj +1 more source
Lie Group Method of the Diffusion Equations
Advances in Mathematical Physics, 2014 The diffusion equation is discretized in spacial direction and transformed into the ordinary differential equations. The ordinary differential equations are solved by Lie group method and the explicit Runge-Kutta method. Numerical results showed that Lie
Jian-Qiang Sun +3 more
doaj +1 more source
Pro-Lie groups which are infinite-dimensional Lie groups [PDF]
arXiv, 2006 A pro-Lie group is a projective limit of a family of finite-dimensional Lie groups. In this note we show that a pro-Lie group $G$ is a Lie group in the sense that its topology is compatible with a smooth manifold structure for which the group operations are smooth if and only if $G$ is locally contractible.
arxiv