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1.
The concepts of solvable and nilpotent Leibniz n-algebra are introduced, and classical results of solvable and nilpotent Lie algebras theory are extended to Leibniz n-algebras category. A homological criterion similar to Stallings Theorem for Lie algebras is obtained in Leibniz n-algebras category by means of the homology with trivial coefficients of Leibniz n-algebras.  相似文献   

2.
本文考查下列高阶有理差分方程xn+1=(α+B1xn-1+B3xn-3+…+B2k+1xn-2k-1)/(A+B0xn+B2xn-2+…+B2kxn-2k,),n=0,1,…,其中k是非负整数,参数α,A,Bi,i=0,1,2,…,2k+1和初始值x-2k-1,x-2k,x-2k+1,…,x0是非负实数.给出充分条件,在此条件下当且仅当∑k+1i=1B2i-1=A时,方程的每个解收敛于方程的一个二周期解.  相似文献   

3.
The present article is devoted to the investigation of properties of Cartan subalgebras and regular elements in Leibniz n-algebras. The relationship between Cartan subalgebras and regular elements of given Leibniz n-algebra and Cartan subalgebras and regular elements of the corresponding factor n-Lie algebra is established.  相似文献   

4.
In this article, we generalize Loday and Pirashvili's [11] computation of the Ext-category of Leibniz bimodules for a simple Lie algebra to the case of a simple (non Lie) Leibniz algebra. Most of the arguments generalize easily, while the main new ingredient is the Feldvoss-Wagemann's cohomology vanishing theorem for semi-simple Leibniz algebras.  相似文献   

5.
J. M. Casas  N. Corral 《代数通讯》2013,41(6):2104-2120
We construct the endofunctor 𝔲𝔠𝔢 between the category of Leibniz algebras which assigns to a perfect Leibniz algebra its universal central extension, and we obtain the isomorphism 𝔲𝔠𝔢Lie(𝔮Lie) ? (𝔲𝔠𝔢Leib(𝔮))Lie, where 𝔮 is a perfect Leibniz algebra satisfying the condition [x, [x, y]] + [[x, y], x] = 0, for all x, y ∈ 𝔮. Moreover, we obtain several results concerning the lifting of automorphisms and derivations in a covering. We also study the relationship between the universal central extension of a semidirect product of perfect Leibniz algebras and the semidirect product of the universal central extension of both of them.  相似文献   

6.
非线性时滞差分议程的全局渐近稳定性   总被引:1,自引:0,他引:1  
In this paper,a sufficient condition for the global asymptotic stability of the solutions of the following nonlinear delay difference equation is obtained,xn 1=xn xn-1xn-2 a/xmxm-1 xn-2 a,n=0,1…,where a∈(0,∞) and the initial values x-2,x-1,x0∈(0,∞).As a special case,a conjecture by Ladas is confirmed.  相似文献   

7.
Yan-Hong Bao  Yu Ye 《代数通讯》2013,41(10):4487-4501
We introduce the enveloping algebra for a Leibniz pair, and show that the category of modules over a Leibniz pair is isomorphic to the category of left modules over its enveloping algebra. Consequently, we show that the cohomology theory for a Leibniz pair introduced by Flato, Gerstenhaber, and Voronov can be interpreted by Ext-groups of modules over the enveloping algebra.  相似文献   

8.
We study deformations of Leibniz algebra morphisms over a commutative local algebra base with 1. We construct the associated deformation cohomology that controls deformations using the cochain complex defining the Leibniz cohomology.  相似文献   

9.
Ashis Mandal 《代数通讯》2013,41(5):2058-2066
In this note, we will show that exact Courant algebras over a Lie algebra 𝔤 can be characterized via Leibniz 2-cocycles, and the automorphism group of a given exact Courant algebra is in a one-to-one correspondence with first Leibniz cohomology space of 𝔤.  相似文献   

10.
设F是一个特征不等于2的域,A是,上的一个可除代数。本文研究了A上多项式环A[x1,X2,…,xn]中理想是有限生成的,以及它的Grobner基;也表明F[x1,x2,…,xn]中有限子集G是F[x1,x2,…,xn]的Griobner基当且仅当G是A[x1,x2,…,xn]中的Grobner基。  相似文献   

11.
《代数通讯》2013,41(3):1377-1386
Abstract

We introduce homology K-vector spaces with trivial coefficients for Leibniz n-algebras and we obtain exact sequences relating them. As a consequence we get a Hopf formula and several results on central extensions of Leibniz n-algebras.  相似文献   

12.
J. Mostovoy 《代数通讯》2013,41(1):185-194
In this note we point out that the definition of the universal enveloping dialgebra for a Leibniz algebra is consistent with the interpretation of a Leibniz algebra as a generalization not of a Lie algebra, but of the adjoint representation of a Lie algebra. From this point of view, the formal integration problem of Leibniz algebras is, essentially, trivial.  相似文献   

13.
Some properties of the second homology and cover of Leibniz algebras are established. By constructing a stem cover, the second Leibniz homology and cover of abelian, Heisenberg Lie algebras and cyclic Leibniz algebras are described. Also, for the dimension of a non-cyclic nilpotent Leibniz algebra L, we obtain dim(HL2(L))≥2.  相似文献   

14.
We study the embedding construction of Lie dialgebras (Leibniz algebras) into conformal algebras. This construction leads to the concept of a conformal representation of Leibniz algebras. We prove that each (finite-dimensional) Leibniz algebra possesses a faithful linear representation (of finite type). As a corollary we give a new proof of the Poincaré-Birkhoff-Witt theorem for Leibniz algebras.  相似文献   

15.
Donald W. Barnes 《代数通讯》2013,41(7):2463-2472
If U is a subnormal subalgebra of a finite-dimensional Leibniz algebra L and M is a finite-dimensional irreducible L-bimodule, then all U-bimodule composition factors of M are isomorphic. If U is a subnormal subalgebra of a finite-dimensional Leibniz algebra L, then the nilpotent residual of U is an ideal of L. Engel subalgebras of finite-dimensional Leibniz algebras are shown to have similar properties to those of Lie algebras. A subalgebra is shown to be a Cartan subalgebra if and only if it is minimal Engel, provided that the field has sufficiently many elements.  相似文献   

16.
17.
Tiffany Burch 《代数通讯》2013,41(8):3622-3625
A converse to Lie's theorem for Leibniz algebras is found and generalized. The result is used to find cases in which the generalized property, called triangulable, is 2-recognizable; that is, if all 2-generated subalgebras are triangulable, then the algebra is also. Triangulability joins solvability, supersolvability, strong solvability, and nilpotentcy as a 2-recognizable property for classes of Leibniz algebras.  相似文献   

18.
ABSTRACT

We describe infinite-dimensional Leibniz algebras whose associated Lie algebra is the Witt algebra and we prove the triviality of low-dimensional Leibniz cohomology groups of the Witt algebra with the coefficients in itself.  相似文献   

19.
We study the nilpotency properties of the Leibniz algebras constructed by means of D-mappings on the algebra of complex square matrices M n (C). In particular, we obtain a criterion for nilpotency of these algebras in terms of the properties of a D-mapping. We prove also that the Leibniz algebras under consideration cannot be simple.  相似文献   

20.
研究三阶有理差分方程x_(n+1)=ax_(n-1)+x_(n-1)x_n/bx_(n-2)+cx_n,n=0,1,2,...的奇点集和解{x_n}_(n=-2)~∞的渐近性,其中a,b,c∈R,初始值x_(-2),x_(-1),x_0∈R.由a,b,c的取值的不同,而得到解的不同的渐近性.  相似文献   

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