共查询到20条相似文献,搜索用时 93 毫秒
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本文研究了李color三系的上同调结构和Nijenhuis算子的问题.利用李三系的上同调和Nijenhuis算子的研究方法,构造出李color三系的上边界算子,获得了李color三系的单参数形式形变.推广了线性映射生成无穷小形变的充分必要条件,同时证明了由一个李color三系的Nijenhuis算子产生的形变是平凡的. 相似文献
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腾文 《数学年刊A辑(中文版)》2024,(1):39-52
本文研究Lie-Yamaguti代数的相对微分算子.首先给出Lie-Yamaguti代数上相对微分算子的概念并给出等价刻画.随后,引入Lie-Yamaguti代数上相对微分算子的上同调.最后,讨论Lie-Yamaguti代数上相对微分算子的无穷小形变. 相似文献
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本文给出了Hom-李代数上新的一系列上边缘算子,证明了这些上边缘算子所对应的上同调群都是同构的.接着,本文研究了这些上边缘算子的性质,得到:向量空间g上的Hom-李代数结构与Λg~*■V上的一系列上边缘算子是一一对应的. 相似文献
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首先证明了有限维Z-阶化李代数上的一个线性算子是Hom-结构的充分必要条件,即它的每个齐次分支也是Hom-结构.然后计算了特征零代数闭域上一类有限维Z-阶化Filiform李代数Qn的齐次Hom-结构,从而决定了Qn的所有Hom-结构. 相似文献
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Hom-李代数是一类满足反对称和Hom-Jacobi等式的非结合代数.扭Heisenberg-Virasoro代数是次数不超过1的微分算子代数的中心扩张,它是一类重要的无限维李代数,与一些曲线的模空间有关.文章主要研究扭Heisenberg-Virasoro代数上Hom-李代数结构,确定了扭Heisenberg-Virasoro代数上存在非平凡的Hom-李代数结构. 相似文献
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蒋志洪 《数学年刊A辑(中文版)》2002,(4)
本文利用广义限制李代数的概念和应用Frobenius代数的一些性质来研究广义限制李代数的广义限制完备上同调,并利用广义限制上同调与通常上同调的关系尝试着给出一种计算系数为不可约模的阶化Cartan型李代数上同调的方法. 相似文献
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阶化Cartan型李代数的上同调 总被引:1,自引:0,他引:1
本文利用广义限制李代数的概念和应用Frobenius代数的一些性质来研究广义限制李代数的广义限制完备上同调,并利用广义限制上同调与通常上同调的关系尝试着给出一种计算系数为不可约模的阶化Cartan型李代数上同调的方法. 相似文献
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本文具体的、系统的研究了Frobenius Hom-代数的二重结构, 并引入了O-算子与Hom-dendriform代数的密切关系.此外,研究Hom-dendriform代数上的Connes余循环的二重结构.最后,给出反对称无穷小Hom-双代数与Hom-dendriform D-双代数的类比关系. 相似文献
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In this paper, we determine all the Rota-Baxter operators of weight zero on semigroup algebras of order two and three with the help of computer algebra. We determine the matrices for these Rota-Baxter operators by directly solving the defining equations of the operators. We also produce a Mathematica procedure to predict and verify these solutions. 相似文献
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This paper studies the concepts of a totally compatible dialgebra and a totally compatible Lie dialgebra,defined to be a vector space with two binary operations that satisfy individual and mixed associativity conditions and Lie algebra conditions respectively.We show that totally compatible dialgebras are closely related to bimodule algebras and semi-homomorphisms.More significantly,Rota-Baxter operators on totally compatible dialgebras provide a uniform framework to generalize known results that Rota-Baxter related operators give tridendriform algebras.Free totally compatible dialgebras are constructed.We also show that a Rota-Baxter operator on a totally compatible Lie dialgebra gives rise to a PostLie algebra,generalizing the fact that a Rota-Baxter operator on a Lie algebra gives rise to a PostLie algebra. 相似文献
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Vsevolod Yu. Gubarev Pavel S. Kolesnikov 《Central European Journal of Mathematics》2013,11(2):226-245
Following a recent work [Bai C., Bellier O., Guo L., Ni X., Splitting of operations, Manin products, and Rota-Baxter operators, Int. Math. Res. Not. IMRN (in press), DOI: 10.1093/imrn/rnr266] we define what is a dendriform dior trialgebra corresponding to an arbitrary variety Var of binary algebras (associative, commutative, Poisson, etc.). We call such algebras di- or tri-Var-dendriform algebras, respectively. We prove in general that the operad governing the variety of di- or tri-Var-dendriform algebras is Koszul dual to the operad governing di- or trialgebras corresponding to Var!. We also prove that every di-Var-dendriform algebra can be embedded into a Rota-Baxter algebra of weight zero in the variety Var, and every tri-Var-dendriform algebra can be embedded into a Rota-Baxter algebra of nonzero weight in Var. 相似文献
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Kurusch Ebrahimi-Fard 《Journal of Pure and Applied Algebra》2008,212(2):320-339
In this paper we study the adjoint functors between the category of Rota-Baxter algebras and the categories of dendriform dialgebras and trialgebras. In analogy to the well-known theory of the adjoint functor between the category of associative algebras and Lie algebras, we first give an explicit construction of free Rota-Baxter algebras and then apply it to obtain universal enveloping Rota-Baxter algebras of dendriform dialgebras and trialgebras. We further show that free dendriform dialgebras and trialgebras, as represented by binary planar trees and planar trees, are canonical subalgebras of free Rota-Baxter algebras. 相似文献
15.
Huihui An & Zhichun Wang 《数学研究通讯:英文版》2016,32(1):57-69
L-octo-algebra with 8 operations as the Lie algebraic analogue of octo-algebra such that the sum of 8 operations is a Lie algebra is discussed. Any octo-algebra is an L-octo-algebra. The relationships among L-octo-algebras, L-quadri-algebras, L-dendriform algebras, pre-Lie algebras and Lie algebras are given. The close relationships between L-octo-algebras and some interesting structures like Rota-Baxter operators, classical Yang-Baxter equations and some bilinear forms satisfying certain conditions are given also. 相似文献
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In this paper, we establish the Composition-Diamond lemma for associative algebras with multiple linear operators. As applications, we obtain Gröbner-Shirshov bases of free Rota-Baxter algebra, free λ-differential algebra and free λ-differential Rota-Baxter algebra, respectively. In particular, linear bases of these three free algebras are respectively obtained, which are essentially the same or similar to the recent results obtained by K. Ebrahimi-Fard-L. Guo, and L. Guo-W. Keigher by using other methods. 相似文献
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In this paper, we introduce a notion of J-dendriform algebra with two operations as a Jordan algebraic analogue of a dendriform
algebra such that the anticommutator of the sum of the two operations is a Jordan algebra. A dendriform algebra is a J-dendriform
algebra. Moreover, J-dendriform algebras fit into a commutative diagram which extends the relationships among associative,
Lie, and Jordan algebras. Their relations with some structures such as Rota-Baxter operators, classical Yang-Baxter equation,
and bilinear forms are given. 相似文献
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从Yang-Baxter簇方程和Volterra积分方程得到的Rota-Baxter簇代数的概念出发,我们引入Rota-Baxter簇系统的概念,推广了Brzezinski提出的Rota-Baxter系统.我们证明这个概念也与结合Yang-Baxter簇对和pre-Lie簇代数有关.此外,作为Rota-Baxter簇系统的一个类比,我们引入平均簇系统的概念,并证明平均簇系统会得到dialgebra簇结构.我们还研究dendriform代数上的Rota-Baxter簇系统,并展示它们如何诱导quadri簇代数结构.最后,我们用Gr\"obner-Shirshov基的方法给出Rota-Baxter簇系统的一个线性基. 相似文献
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RunQiang Jian 《中国科学 数学(英文版)》2014,57(11):2321-2328
We propose the notion of Hopf module algebra and show that the projection onto the subspace of coinvariants is an idempotent Rota-Baxter operator of weight-1. We also provide a construction of Hopf module algebras by using Yetter-Drinfeld module algebras. As an application,we prove that the positive part of a quantum group admits idempotent Rota-Baxter algebra structures. 相似文献