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1.
We investigate the nilpotence of a Malcev algebra M and of its standard enveloping Lie algebra L(M)=M D(M, M). The main result shows that an ideal A of M is nilpotent in M if and only if the corresponding ideal Ⅰ(A) = A D(A, M)is nilpotent in L(M). 相似文献
2.
V. M. Petrogradsky 《代数通讯》2013,41(3):918-928
We study Lie nilpotent varieties of associative algebras. We explicitly compute the codimension growth for the variety of strong Lie nilpotent associative algebras. The codimension growth is polynomial and found in terms of Stirling numbers of the first kind. To achieve the result we take the free Lie algebra of countable rank L(X), consider its filtration by the lower central series and shift it. Next we apply generating functions of special type to the induced filtration of the universal enveloping algebra U(L(X)) = A(X). 相似文献
3.
N. A. Koreshkov 《Russian Mathematics (Iz VUZ)》2008,52(8):20-27
In this paper, we study some properties of algebras of associative type introduced in previous papers of the author. We show that a finite-dimensional algebra of associative type over a field of zero characteristic is homogeneously semisimple if and only if a certain form defined by the trace form is nonsingular. For a subclass of algebras of associative type, it is proved that any module over a semisimple algebra is completely reducible. We also prove that any left homogeneous ideal of a semisimple algebra of associative type is generated by a homogeneous idempotent. 相似文献
4.
WANG Gui-dong 《数学季刊》2005,20(4):423-429
In this paper, we mainly concerned about the nilpotence of Lie triple algebras. We give the definition of nilpotence of the Lie triple algebra and obtained that if Lie triple algebra is nilpotent, then its standard enveloping Lie algebra is nilpotent. 相似文献
5.
本文加深了Hopenwasser和Paulsen关于有向图代数中Lie理想的一个结果,证明了有向图代数A的一个线性子空间是A的Lie理想当且仅当存在A的一个结合理想Y及A的masa D的一个子代数E,使得(Y)~0■■Y+E,其中(Y)~0是Y中迹为零的所有元的集合. 相似文献
6.
π-complemented algebras are defined as those algebras (not necessarily associative or unital) such that each annihilator ideal is complemented by other annihilator ideal. Let A be a semiprime algebra. We prove that A is π-complemented if, and only if, every idempotent in the extended centroid of A lies in the centroid of A. We also show the existence of a smallest π-complemented subalgebra of the central closure of A containing A. In the case that A is a C*-algebra, this subalgebra turns out to be a norm dense *-subalgebra of the bounded central closure of A. It follows that a C*-algebra is boundedly centrally closed if, and only if, it is π-complemented. 相似文献
7.
A Noetherian (Artinian) Lie algebra satisfies the maximal (minimal) condition for ideals.Generalisations include quasi-Noetherian and quasi-Artinian Lie algebras.We study conditions on prime ideals relating these properties.We prove that the radicalof any ideal of a quasi-Artinian Lie algebra is the intersection of finitely many prime ideals,and an ideally finite Lie algebra is quasi-Noetherian if and only if it is qussi-Artinian.Both properties are equivalent to soluble-by-finite.We also prove a structure theorem for serially finite Artinian Lie algebras. 相似文献
8.
广义a-结合BCI-代数 总被引:3,自引:0,他引:3
张富林 《纯粹数学与应用数学》1997,(2)
引入了广义a-结合BCI-代数的概念,研究了BCI-代数的p-半单部分与广义a-结合部分的关系.并将p-半单BCI-代数的若干重要性质推广到广义a-结合BCI-代数上.最后我们证明了每个广义a-结合BCI-代数可确定一个交换偏序幺半群.本文结果表明文[1]的正则BCI-代数与p-半单BCI-代数是一致的. 相似文献
9.
HBa(D)空间的内插定理 总被引:2,自引:0,他引:2
刘官厅 《应用泛函分析学报》2000,2(3):218-223
研究了一类由H^p空间构成的Ba空间的内插性质,给出了H^Ba(D)空间的三个内插定理。 相似文献
10.
Yong Zhang 《Journal of Functional Analysis》2002,191(1):123-131
We show that every closed ideal of a Segal algebra on a compact group admits a central approximate identity which has the property, called condition (U), that the induced multiplication operators converge to the identity operator uniformly on compact sets of the ideal. This result extends a known one due to H. Reiter who has considered the problem under the condition that the Segal algebra is symmetric. We prove further that a closed right ideal of a Segal algebra on a compact group admits a left approximate identity satisfying condition (U) if and only if it is approximately complemented as a subspace of the Segal algebra; if in addition the Segal algebra is symmetric, then a closed left ideal admits a right approximate identity satisfying condition (U) if and only if it is approximately complemented. 相似文献
11.
R. Dastanpour 《代数通讯》2017,45(7):2889-2898
We present a generalization of the ascending and descending chain condition on one-sided ideals by means of divisibility on chains. We say that a ring R satisfies ACCd on right ideals if in every ascending chain of right ideals of R, each right ideal in the chain, except for a finite number of right ideals, is a left multiple of the following one; that is, each right ideal in the chain, except for a finite number, is divisible by the following one. We study these rings and prove some results about them. Dually, we say that a ring R satisfies DCCd on right ideals if in every descending chain of right ideals of R, each right ideal in the chain, except for a finite number of right ideals, is divisible by the previous one. We study these conditions on rings, in general and in special cases. 相似文献
12.
A left-symmetric algebra is said to be filiform if both natural descending series induced by the product tend to zero, but as slow as possible. This is the analogue of the more common notion for Lie algebras. In this paper, we develop some theoretical aspects of this class of left-symmetric algebras and we also present a classification of them up till dimension 5. 相似文献
13.
Given a finite, simple, vertex-weighted graph, we construct a graded associative (noncommutative) algebra, whose generators correspond to vertices and whose ideal of relations has generators that are graded commutators corresponding to edges. We show that the Hilbert series of this algebra is the inverse of the clique polynomial of the graph. Using this result it easy to recognize if the ideal is inert, from which strong results on the algebra follow. Noncommutative Gr?bner bases play an important role in our proof. There is an interesting application to toric topology. This algebra arises naturally from a partial product of spheres, which is a special case of a generalized moment?Cangle complex. We apply our result to the loop-space homology of this space. 相似文献
14.
Cristina Draper Antonio Fernández López Esther García Miguel Gómez Lozano 《Journal of Algebra》2008,319(6):2372-2394
We define the socle of a nondegenerate Lie algebra as the sum of all its minimal inner ideals. The socle turns out to be an ideal which is a direct sum of simple ideals, and satisfies the descending chain condition on principal inner ideals. Every classical finite dimensional Lie algebra coincides with its socle, while relevant examples of infinite dimensional Lie algebras with nonzero socle are the simple finitary Lie algebras and the classical Banach Lie algebras of compact operators on an infinite dimensional Hilbert space. This notion of socle for Lie algebras is compatible with the previous ones for associative algebras and Jordan systems. We conclude with a structure theorem for simple nondegenerate Lie algebras containing abelian minimal inner ideals, and as a consequence we obtain that a simple Lie algebra over an algebraically closed field of characteristic 0 is finitary if and only if it is nondegenerate and contains a rank-one element. 相似文献
15.
16.
Simple algebras of Weyl type 总被引:9,自引:0,他引:9
Over a fieldF of arbitrary characteristic, we define the associative and the Lie algebras of Weyl type on the same vector spaceA[D] =A⊗F[D] from any pair of a commutative associative algebra,A with an identity element and the polynomial algebraF[D] of a commutative derivation subalgebraD ofA We prove thatA[D], as a Lie algebra (modulo its center) or as an associative algebra, is simple if and only ifA isD-simple andA[D] acts faithfully onA. Thus we obtain a lot of simple algebras.
Su, Y., Zhao, K., Second cohornology group of generalized Witt type Lie algebras and certain representations, submitted to
publication 相似文献
17.
令Cq:=Cq[t1±1,t2±1,t3±1]为量子环面结合代数,Lq=Cq/C为量子环面李代数。本文定义了一个与q=(qij)i,j=13相关的指数方程体系,称之为Cq的特征方程组。通过这个特征方程组,证明了Lq是非单的当且仅当特征方程组在Z3中有非零解。对于|q|=0,证明了在Cq中存在一个极大交换子代数I,并且I严格包含中心Z(Cq)。同时文中也指出,对于|q|≠0,在Cq中不存在这样的子代数。 相似文献
18.
Maria Gorelik 《Journal of the American Mathematical Society》2002,15(1):113-165
In this article we prove that for a basic classical Lie superalgebra the annihilator of a strongly typical Verma module is a centrally generated ideal. For a basic classical Lie superalgebra of type I we prove that the localization of the enveloping algebra by a certain central element is free over its centre.
19.
Má tyá s Domokos Vesselin Drensky 《Transactions of the American Mathematical Society》1998,350(7):2797-2811
Nagata gave a fundamental sufficient condition on group actions on finitely generated commutative algebras for finite generation of the subalgebra of invariants. In this paper we consider groups acting on noncommutative algebras over a field of characteristic zero. We characterize all the T-ideals of the free associative algebra such that the algebra of invariants in the corresponding relatively free algebra is finitely generated for any group action from the class of Nagata. In particular, in the case of unitary algebras this condition is equivalent to the nilpotency of the algebra in Lie sense. As a consequence we extend the Hilbert-Nagata theorem on finite generation of the algebra of invariants to any finitely generated associative algebra which is Lie nilpotent. We also prove that the Hilbert series of the algebra of invariants of a group acting on a relatively free algebra with a non-matrix polynomial identity is rational, if the action satisfies the condition of Nagata.
20.
Complemented Lie algebras are introduced in this paper (a notion similar to that studied by O. Loos and E. Neher in Jordan pairs). We prove that a Lie algebra is complemented if and only if it is a direct sum of simple nondegenerate Artinian Lie algebras. Moreover, we classify simple nondegenerate Artinian Lie algebras over a field of characteristic 0 or greater than 7, and describe the Lie inner ideal structure of simple Lie algebras arising from simple associative algebras with nonzero socle. 相似文献