Pre-Lie algebras, also called Vinberg algebras, have become an important tool in combinatorics, differential geometry, the theory of operads and in various application domains such as perturbative quantum field theory or numerical analysis, to quote only a few. They generate a special class of Lie...
A short survey on pre-Lie algebras We give an account of fundamental properties of pre-Lie algebras, and provide several examples borrowed from various domains of Mathematics and Physics : A... D Manchon 被引量: 68发表: 2009年 Enhanced preliminary group classification of a class of generalized...
1) quasi-pre-Lie algebras quasi-pre-Lie代数2) Lie algebra Lie代数 1. An extension of Lie algebra and a related integrable system; 推广的一类Lie代数及其相关的一族可积系统 2. Lie algebraic method for the vibrational excited states of a SO 2 molecule has been studied. 利用Lie代数方法...
We not only study the invertible Rota-Baxter operators on pre-Lie algebras, but also give some interesting construction of Rota-Baxter operators. Furthermore, we give all Rota-Baxter operators on 2-dimensional complex pre-Lie algebras and some examples in higher dimensions. 1 Introduction Rota-...
hopfalgebrastreesliefamiliesalgebra arXiv:math/0402022v1[math.QA]2Feb2004FamiliesofHopfalgebrasoftreesandpre-LiealgebrasPepijnvanderLaanandIekeMoerdijk1stFebruary2008AbstractUsingmethodsfrom[10],westudyfamiliesofHopfalgebrastructuresoncolouredtrees.1IntroductionOverthepastyearsmoreandmoreexamplesofcombinatorialHopfal-...
分类号:学校代码:10165密级:学号:201711010499BiHom-pre-Lie代数的双模BimodulesofBiHom-pre-LieAlgebras2020年6月作者姓名:***科、专业:基础数学研究方向:李代数导师姓名:***位论文独创性声明本人承诺:所呈交的学位论文是本人在导师指导下所取得的研究成果。论文中除特别加以标注和致谢的地方外,不包含他人和其他机构...
Gamkrelidze of monomial bases in free pre-Lie algebras. We describe the matrix of the monomial basis vectors in terms of the rooted trees basis exhibited by F. Chapoton and M. Livernet. Also, we show that this matrix is unipotent and we find an explicit expression for its coefficients, ...
We give a simple characterization of Lie elements in free pre-Lie algebras as elements of the kernel of a map between spaces of trees. We explain how this result is related to natural operations on the Chevalley-Eilenberg complex of a Lie algebra. We also indicate a possible relation to Lo...
Ennea-algebras Such algebras allow the construction of nested dendriform trialgebras and are related to pre-Lie algebras, t-infinitesimal bialgebras and t-Baxter operators... P Leroux - 《Journal of Algebra》 被引量: 65发表: 2003年 Infinitesimal Hopf Algebras and the cd-Index of Polytopes Infi...
We construct an associative product on the symmetric module S(L) of any pre-Lie algebra L. Then we proove that in the case of rooted trees our construction is dual to that of Connes and Kreimer. We also show that symmetric brace algebras and pre-Lie alge