Results 41 to 50 of about 107,381 (262)

Cohomology and Crossed Modules of Modified Rota–Baxter Pre-Lie Algebras

Mathematics
The goal of the present paper is to provide a cohomology theory and crossed modules of modified Rota–Baxter pre-Lie algebras. We introduce the notion of a modified Rota–Baxter pre-Lie algebra and its bimodule.
Fuyang Zhu, Wen Teng
doaj   +1 more source

Algebras of Complete Hörmander Vector Fields, and Lie-Group Construction

Bruno Pini Mathematical Analysis Seminar, 2014
The aim of this note is to characterize the Lie algebras g of the analytic vector fields in RN which coincide with the Lie algebras of the (analytic) Lie groups defined on RN (with its usual differentiable structure). We show that such a characterization
Andrea Bonfiglioli
doaj   +1 more source

The second cohomology groups of nilpotent orbits in classical Lie algebras [PDF]

Kyoto Journal of Mathematics, 2016
The second de Rham cohomology groups of nilpotent orbits in non-compact real forms of classical complex simple Lie algebras are explicitly computed. Furthermore, the first de Rham cohomology groups of nilpotent orbits in non-compact classical simple Lie ...
I. Biswas, Pralay Chatterjee, C. Maity
semanticscholar   +1 more source

Lie Groups and Lie Algebras [PDF]

, 2000
A Lie group is a group G that at the same time is a finite-dimensional manifold of differentiability class C2, in such a way that the two group operations of G: $$ \mu :\;\left( {x,y} \right) \mapsto xy:\;G \times G \to G\quad \left( {multiplication} \right)$$ (1.1.1) $$\iota :\;x \mapsto {x^{ - 1}}\quad :G \to G\quad \left( {inversion ...
Johannes J. Duistermaat, J. A. C. Kolk
openaire   +4 more sources

Generalisation of affine Lie algebras on compact real manifolds

SciPost Physics Proceedings, 2023
We report on recent work concerning a new type of generalised Kac-Moody algebras based on the spaces of differentiable mappings from compact manifolds or homogeneous spaces onto compact Lie groups.
Rutwig Campoamor-Stursberg, Marc de Montigny, Michel Rausch de Traubenberg
doaj   +1 more source

The Recursive Forward Dynamics of Flexible Mechanical Systems

MATEC Web of Conferences, 2016
Lie groups and Lie algebras are used to study the recursive dynamics of flexible multi-body systems. First the adjoint transformations and adjoint operators of Lie groups and Lie algebras are discussed.
Shao Bing, Yuan Entao
doaj   +1 more source

On Hopf 2-algebras

, 2009
Our main goal in this paper is to translate the diagram relating groups, Lie algebras and Hopf algebras to the corresponding 2-objects, i.e. to categorify it.
Fregier, Yael, Wagemann, Friedrich
core   +2 more sources

Lie algebras and torsion groups with identity [PDF]

, 2016
We prove that a finitely generated Lie algebra $L$ such that (i) every commutator in generators is ad-nilpotent, and (ii) $ L$ satisfies a polynomial identity, is nilpotent.
E. Zelmanov
semanticscholar   +1 more source

Representations and cohomologies of modified λ-differential Hom-Lie algebras

AIMS Mathematics
In this paper, we introduce the concept and representations of modified $ \lambda $-differential Hom-Lie algebras. We then develop the cohomology of modified $ \lambda $-differential Hom-Lie algebras with coefficients in a suitable representation.
Yunpeng Xiao , Wen Teng
doaj   +1 more source

Octonions and exceptional Lie algebras [PDF]

, 2020
It is well known that octonions (both real and complex) are very involved in the structure of the exceptional Lie algebras. We will explore several aspects of this relationship: how octonions provide models of the exceptional Lie algebras ...
Draper-Fontanals, Cristina
core