共查询到20条相似文献,搜索用时 750 毫秒
1.
袁鹤 《数学年刊A辑(中文版)》2018,39(2):163-172
研究了广义矩阵代数上的一类李导子,证明了广义矩阵代数上李导子可以表示成一个导子和一个中心映射之和,并将这个结果应用到全矩阵代数上. 相似文献
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In this paper we introduce the notion of Jordan socle for nondegenerate Lie algebras, which extends the definition of socle given in [A. Fernández López et al., 3-Graded Lie algebras with Jordan finiteness conditions, Comm. Algebra, in press] for 3-graded Lie algebras. Any nondegenerate Lie algebra with essential Jordan socle is an essential subdirect product of strongly prime ones having nonzero Jordan socle. These last algebras are described, up to exceptional cases, in terms of simple Lie algebras of finite rank operators and their algebras of derivations. When working with Lie algebras which are infinite dimensional over an algebraically closed field of characteristic 0, the exceptions disappear and the algebras of derivations are computed. 相似文献
4.
Pao-Kuei Liau 《Linear algebra and its applications》2011,435(1):67-76
We characterize generalized Lie derivations on skew elements of prime algebras A with involution, provided that A does not satisfy polynomial identities of low degree. The analogous result for matrix algebras is also described. 相似文献
5.
Jianhua Zhou 《Linear algebra and its applications》2000,320(1-3):97-114
The structure of the Lie algebras with almost dimensionally nilpotent inner derivations is studied. It is proved that, if the base field is of characteristic 0, then, when d>6 is odd, there exist just two d-dimensional Lie algebras; when d>6 is even, there exists just one d-dimensional Lie algebra such that these Lie algebras are nonsolvable and have some almost dimensionally nilpotent inner derivations. 相似文献
6.
Hao Chen 《Proceedings of the American Mathematical Society》1997,125(11):3133-3135
An example is given to show that not every derivation in the nilradical of the Lie algebra of derivations of moduli algebras can be liftable and the dimension of the nilradical of the Lie algebra of derivations of moduli algebras is not a topological invariant for an isolated hypersurface singularity.
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The Lie algebra of Cartan type H which occurs as a subalgebra of the Lie algebra of derivations of the polynomial algebra was generalized by the first author to a class which included a subalgebra of the derivations of the Laurent polynomials
. We show in this paper that these generalizations of Cartan type H algebras are isomorphic to certain generalizations of the classical algebra of Poisson brackets, and that it can be generalized
further. In turn, these algebras can be recast in a form that is an adaption of a class of Lie algebras of characteristic
p that was defined in 1958 be R. Block. A further generalization of these algebras is the main topic of this paper. We show
when these algebras are simple, find their derivations, and determine all possible isomorphisms between two of these algebras.
Received December 20, 1996; in final form September 15, 1997 相似文献
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We study the Lie structure of graded associative algebras. Essentially, we analyze the relation between Lie and associative graded ideals, and between Lie and associative graded derivations. Gathering together results on both directions, we compute maximal graded algebras of quotients of graded Lie algebras that arise from associative algebras. We also show that the Lie algebra Der gr (A) of graded derivations of a graded semiprime associative algebra is strongly non-degenerate (modulo a certain ideal containing the center of Der gr (A)). 相似文献
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Ualbai Umirbaev 《代数通讯》2017,45(7):2809-2820
A structure of a left-symmetric algebra on the set of all derivations of a free algebra is introduced such that its commutator algebra becomes the usual Lie algebra of derivations. Left and right nilpotent elements of left-symmetric algebras of derivations are studied. Simple left-symmetric algebras of derivations and Novikov algebras of derivations are described. It is also proved that the positive part of the left-symmetric algebra of derivations of a free nonassociative symmetric m-ary algebra in one free variable is generated by one derivation and some right nilpotent derivations are described. 相似文献
11.
单扩张型Lie Rinehart代数的分类定理 总被引:1,自引:1,他引:0
定义单扩张型Lie Rinehart代数,从而给出一种通过导子构造Lie Rinehart代数的途径.指出这是一种特殊的作用Lie Rinehart代数.在系数环是没有零因子的交换代数的前提下,给出单扩张型Lie Rinehart代数的完全分类定理.特别的,证明多项式环上的任何非平凡作用Lie Rinehart代数必然是单扩张型的,并给出其标准型. 相似文献
12.
作者对秩为2的无挠的李共形代数进行了刻画.在这些代数中,作者主要关注Virasoro-型李共形代数.并且,作者描述了一种特殊Virasoro-型李共形代数的共形导子、秩为1的自由共形模和中心扩张. 相似文献
13.
Zha Jianguo 《东北数学》1998,(4)
1.InfiniteRankAfineLieAlgebrasg(X)andg(X)WerecalthedefinitionofinfiniterankafineLiealgebrasandtheirfundamentalstructure.Agene... 相似文献
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We study étale descent of derivations of algebras with values in a module. The algebras under consideration are twisted forms of algebras over rings, and apply to all classes of algebras, notably associative and Lie algebras, such as the multiloop algebras that appear in the construction of extended affine Lie algebras. The main result is Theorem 2.7. 相似文献
15.
H. L. Huru 《Russian Mathematics (Iz VUZ)》2008,52(4):65-75
We study quantizations of braided symmetric and exterior algebras of graded vector spaces and of braided derivations on these
algebras. We find quantizations of braided Lie algebras by considering quantizations of derivations on their braided exterior
algebra.
The text was submitted by the author in English. 相似文献
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Lie Derivations of Triangular Algebras 总被引:8,自引:0,他引:8
Wai-Shun Cheung 《Linear and Multilinear Algebra》2003,51(3):299-310
We investigate Lie derivations on a class of algebras called triangular algebras. In particular, we give sufficient conditions such that every Lie derivation on such an algebra is a sum of derivation on and a mapping from to its centre. 相似文献
18.
In this article,the authors obtain some results concerning derivations of finitely generated Lie color algebras and discuss the relation between skew derivation space SkDer(L)and central extension H^2(L,F)on some Lie color algebras.Meanwhile,they generalize the notion of double extension to quadratic Lie color algebras,a sufficient condition for a quadratic Lie color algebra to be a double extension and further properties are given. 相似文献
19.
Generalized Lie derivations on triangular algebras 总被引:1,自引:0,他引:1
Dominik Benkovi? 《Linear algebra and its applications》2011,434(6):1532-1544
Let A be a unital algebra and let M be a unitary A-bimodule. We consider generalized Lie derivations mapping from A to M. Our results are applied to triangular algebras, in particular to nest algebras and (block) upper triangular matrix algebras. We prove that under certain conditions each generalized Lie derivation of a triangular algebra A is the sum of a generalized derivation and a central map which vanishes on all commutators of A. 相似文献
20.
苏育才 《中国科学A辑(英文版)》2003,46(3):346-354
A class of the associative and Lie algebras A[D] = A F[D] of Weyl type are studied, where A is a commutative associative algebra with an identity element over a field F of characteristic zero, and F[D] is the polynomial algebra of a finite dimensional commutative subalgebra of locally finite derivations of A such that A is D-simple. The derivations of these associative and Lie algebras are precisely determined. 相似文献