共查询到20条相似文献,搜索用时 31 毫秒
1.
ON THE VARIATIONS OF G_2 总被引:2,自引:0,他引:2
In [1], Shen Guangyu constructed several classes of new simple Lie algebras of characteristic 2, which are called the variations of G2. In this paper, the authors investigate their derivation algebras. It is shown that G2 and its variations all possess unique nondegenerate associative forms. The authors also find some nonsingular derivations of ViG for i = 3,4, 5, 6, and thereby construct some left-symmetric structures on Vi G for i = 3,4,5,6. Some errors about the variations of sl(3, F) in [1] are corrected. 相似文献
2.
Mohammed Guediri 《代数通讯》2013,41(7):2919-2937
We discuss locally simply transitive affine actions of Lie groups G on finite-dimensional vector spaces such that the commutator subgroup [G, G] is acting by translations. In other words, we consider left-symmetric algebras satisfying the identity [x, y]·z = 0. We derive some basic characterizations of such left-symmetric algebras, and we highlight their relationships with the so-called Novikov algebras and derivation algebras. 相似文献
3.
On Spectral Integral Variations of Graphs 总被引:4,自引:0,他引:4
Fan Yizheng 《Linear and Multilinear Algebra》2002,50(2):133-142
Let G be a general graph. The spectrum S ( G ) of G is defined to be the spectrum of its Laplacian matrix. Let G + e be the graph obtained from G by adding an edge or a loop e . We study in this paper when the spectral variation between G and G + e is integral and obtain some equivalent conditions, through which a new Laplacian integral graph can be constructed from a known Laplacian integral graph by adding an edge. 相似文献
4.
Fan Yizheng 《Linear and Multilinear Algebra》2013,61(2):133-142
Let G be a general graph. The spectrum S ( G ) of G is defined to be the spectrum of its Laplacian matrix. Let G + e be the graph obtained from G by adding an edge or a loop e . We study in this paper when the spectral variation between G and G + e is integral and obtain some equivalent conditions, through which a new Laplacian integral graph can be constructed from a known Laplacian integral graph by adding an edge. 相似文献
5.
Let R be a noncommutative prime ring and d, δ two nonzero derivations of R. If δ([d(x), x] n ) = 0 for all x ∈ R, then char R = 2, d 2 = 0, and δ = αd, where α is in the extended centroid of R. As an application, if char R ≠ 2, then the centralizer of the set {[d(x), x] n | x ∈ R} in R coincides with the center of R. 相似文献
6.
7.
《Expositiones Mathematicae》2022,40(4):845-869
We make several observations relating the Lie algebra , associative 3-planes, and subalgebras. Some are likely well-known but not easy to find in the literature, while other results are new. We show that an element cannot have rank 2, and if it has rank 4 then its kernel is an associative subspace. We prove a canonical form theorem for elements of . Given an associative 3-plane in , we construct a Lie subalgebra of that is isomorphic to . This subalgebra differs from other known constructions of subalgebras of determined by an associative 3-plane. These are results of an NSERC undergraduate research project. The paper is written so as to be accessible to a wide audience. 相似文献
8.
Cheng-Kai Liu 《代数通讯》2013,41(7):2396-2404
Let R be a commutative ring, and D a Lie subring and an R-submodule of Der(R) such that R is D-semiprime (or D-prime). We investigate the structure of the ideals of D as Lie rings. As a consequence, we give a necessary and sufficient condition for the ideals of D to be semiprime (or prime, respectively) Lie rings. 相似文献
9.
《Journal of Pure and Applied Algebra》2022,226(11):107105
In this paper we study the generators of the module of derivations of certain rings and obtain bounds on their minimum number of generators. We will also study minimum number of generators of divisorial ideals of two dimensional rings of invariants, in particular the canonical modules of these rings. 相似文献
10.
In this article, by choosing appropriate basis, we give a complete classification of 2-step nilpotent Lie algebras of dimension 8 with 2-dimensional center. 相似文献
11.
《代数通讯》2013,41(11):4387-4413
Abstract In the paper, the deriviation algebras of the associative algebras of the one-variable (resp. multivariable) q-differential operators and of their corresponding Lie algebras are determined. The completeness of the derivation algebras of the algebras of q-differential operators is also discussed. Finally, we calculate H 2(𝒟 q (n)?, C) for n ≥ 1, as well as H 2(g l n (𝒟 q ), C) under the assumption that q is transcendental over the rational numbers field Q. 相似文献
12.
On the product of two generalized derivations 总被引:2,自引:0,他引:2
Mohamed Barraa Steen Pedersen 《Proceedings of the American Mathematical Society》1999,127(9):2679-2683
Two elements and in a ring determine a generalized derivation on by setting for any in . We characterize when the product is a generalized derivation in the cases when the ring is the algebra of all bounded operators on a Banach space , and when is a -algebra . We use these characterizations to compute the commutant of the range of .
13.
Spectral Integral Variations of Degree Maximal Graphs 总被引:3,自引:0,他引:3
Fan Yizheng 《Linear and Multilinear Algebra》2003,51(2):147-154
The concept of the spectral integral variation was introduced by Fan [Fan Yizheng (2002). On spectral integral variations of graphs. Linear and Multilinear Algebra , 50 , 133-142] to study the general graphs with all changed eigenvalues moving up by integers when an edge is added. Here we consider the spectral integral variations of maximal graphs G , and successfully give an equivalent condition for the spectral integral variation of G occurring in two places by adding an edge e . We also characterize whether the graph G + e is maximal so that an explicit interpretation of the above condition is obtained, where G + e denotes the graph obtained from G by adding an edge e . 相似文献
14.
Fan Yizheng 《Linear and Multilinear Algebra》2013,61(2):147-154
The concept of the spectral integral variation was introduced by Fan [Fan Yizheng (2002). On spectral integral variations of graphs. Linear and Multilinear Algebra , 50 , 133-142] to study the general graphs with all changed eigenvalues moving up by integers when an edge is added. Here we consider the spectral integral variations of maximal graphs G , and successfully give an equivalent condition for the spectral integral variation of G occurring in two places by adding an edge e . We also characterize whether the graph G + e is maximal so that an explicit interpretation of the above condition is obtained, where G + e denotes the graph obtained from G by adding an edge e . 相似文献
15.
Bangteng Xu 《代数通讯》2013,41(5):1279-1297
ABSTRACT A commutative algebra with the identity (a * b) * (c * d) ? (a * d) * (c * b) = (a, b, c) * d ? (a, d, c) * b is called Novikov–Jordan. Example: K[x] under multiplication a * b = ?(ab) is Novikov–Jordan. A special identity for Novikov–Jordan algebras of degree 5 is constructed. Free Novikov–Jordan algebras with q generators are exceptional for any q ≥ 1. 相似文献
16.
We study the unitary subgroupV ?(F2 G) in the group algebras F2 Gof 2-groups of maximal class over the field F2of two elements. We show that there does not exist a normal complement to Gin V ?(F2 G) if and only if Gis the dihedral group of order 2n(n≥ 5) or the semidihedral group of order 2n(n≥5). We also describe V ?(F2 G) when the subgroup Ghas order 8 and 16 and in this case there exist a normal complement of Gin V ?(F2 G). 相似文献
17.
Vladimir G. Tkachev 《代数通讯》2019,47(3):1057-1066
18.
Yi-Fang Kang 《代数通讯》2013,41(1):82-93
In this article, we construct a faithful representation with the lowest dimension for every complex Lie algebra in dimension ≤ 4. In particular, in our construction, in the case that the faithful representation has the same dimension of the Lie algebra, it can induce an étale affine representation with base zero which has a natural and simple form and gives a compatible left-symmetric algebra on the Lie algebra. Such affine representations do not contain any nontrivial one-parameter subgroups of translation. 相似文献
19.
20.
A. P. Pojidaev 《代数通讯》2013,41(10):3593-3608
Derivations of the simple ternary Malcev algebra M 8 and its algebra of multiplications are described. 相似文献