共查询到20条相似文献,搜索用时 0 毫秒
1.
Gábor P. Nagy 《代数通讯》2013,41(2):549-555
ABSTRACT Let (A, ?) be a structurable algebra. Then the opposite algebra (A op , ?) is structurable, and we show that the triple system B op A(x, y, z):=Vopx,y(z)=x(y¯z)+z(y¯x)?y(x¯z), x, y, z ∈ A, is a Kantor triple system (or generalized Jordan triple system of the second order) satisfying the condition (A). Furthermore, if A=𝔸1?𝔸2 denotes tensor products of composition algebras, (?) is the standard conjugation, and (∧) denotes a certain pseudoconjugation on A, we show that the triple systems B op 𝔸1?𝔸2 ( x , y¯∧, z) are models of compact Kantor triple systems. Moreover these triple systems are simple if (dim𝔸1, dim𝔸2) ≠ (2, 2). In addition, we obtain an explicit formula for the canonical trace form for compact Kantor triple systems defined on tensor products of composition algebras. 相似文献
2.
Compact Exceptional Simple Kantor Triple Systems Defined on Tensor Products of Composition Algebras∗
Daniel Mondoc 《代数通讯》2013,41(11):3699-3712
In this article we give the classification of compact exceptional simple Kantor triple systems defined on tensor products of composition algebras A = 1? 2 such that their Kantor algebras ?(φ, A) are real forms of exceptional simple Lie algebras. 相似文献
3.
4.
Lei LIU 《数学年刊B辑(英文版)》2018,39(5):817-828
Let A be a von Neumann algebra with no central abelian projections. It is proved that if an additive map δ :A → A satisfies δ([[a, b], c]) = [[δ(a), b], c] + [[a, δ(b)], c] +[[a, b], δ(c)] for any a, b, c∈ A with ab = 0(resp. ab = P, where P is a fixed nontrivial projection in A), then there exist an additive derivation d from A into itself and an additive map f :A → ZA vanishing at every second commutator [[a, b], c] with ab = 0(resp.ab = P) such that δ(a) = d(a) + f(a) for any a∈ A. 相似文献
5.
6.
设?=Tri(A,M,B)为三角代数,?={T∈?:T~2=0}且δ:?→?是一个映射(没有可加或线性假设).证明了:如果对任意A,B,C∈?且ABC∈?,有δ(ABC)=δ(A)BC+Aδ(B)C+ABδ(C),则δ是一个可加导子·作为应用,得到了上三角矩阵代数和套代数上此类非全局三重可导映射的具体形式. 相似文献
7.
研究了限制李三系的半单元的一些重要性质,给出了若干个限制李三系是可换的条件,得到了限制李三系的有环面元基的几个条件,刻划了限制李三系的Frattini p-子系的一些性质.同时,研究了中心为零的所有元素是半单元的限制李三系的一些重要性质. 相似文献
8.
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
9.
Terrell L. Hodge Brian J. Parshall 《Transactions of the American Mathematical Society》2002,354(11):4359-4391
In this paper, we take a new look at the representation theory of Lie triple systems. We consider both ordinary Lie triple systems and restricted Lie triple systems in the sense of [14]. In a final section, we begin a study of the cohomology of Lie triple systems.
10.
M. Palese 《Theoretical and Mathematical Physics》2005,144(1):1014-1021
We solve the Backlund problem for both the compact and noncompact versions of the Ishimori (2+1)-dimensional nonlinear spin model. In particular, we realize the arising Backlund algebra in the form of an infinite-dimensional loop Lie algebra of the Kac-Moody type.This note is part of joint research work with E. Winterroth.__________Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 144, No. 1, pp. 153–161, July, 2005. 相似文献
11.
In this article, we introduce the notion of system of quotients of Lie triple systems and investigate some properties which can be lifted from a Lie triple system to its systems of quotients. We relate the notion of Lie triple system of Martindale-like quotients with respect to a filter of ideals and the notion of system of quotients, and prove that the system of quotients of a Lie triple system is equivalent to the algebra of quotients of a Lie algebra in some sense, and these allow us to construct the maximal system of quotients for nondegenerate Lie triple systems. 相似文献
12.
We study sequential convergences defined on a Boolean algebra by systems of maximal filters. We describe the order properties of the system of all such convergences. We introduce the category of 2-generated convergence Boolean algebras and generalize the construction of Novak sequential envelope to such algebras. 相似文献
13.
14.
J. C. Motta Ferreira 《代数通讯》2013,41(9):3209-3216
In this article we prove that, if (U, ω) is a finite dimensional baric algebra of (γ, δ) type over a field F of characteristic ≠ 2,3,5 such that γ2 ? δ2 + δ = 1 and δ ≠ 0,1, then rad(U) = R(U) ∩ (bar(U))2, where R(U) is the nilradical (maximal nil ideal) of U. 相似文献
15.
In this paper, the authors study a class of generalized intersection matrix Lie algebras gim(Mn), and prove that its every finite-dimensional semisimple quotient is of type M(n, a, c, d). Particularly, any finite dimensional irreducible gim(Mn) module must be an irreducible module of Lie algebra of type M(n, a, c, d) and any finite dimensional irreducible module of Lie algebra of type M(n, a, c, d) must be an irreducible module of gim(Mn). 相似文献
16.
17.
主要把群的Frattini理论发展到限制李三系,得到限制李三系的Frattini-子系、Frattini p-子系的性质,给出Frattini p-子系为零时限制李三系的分解. 相似文献
18.
设u=Tri(A,M,B)是三角代数.证明了在一般的假设下,如果线性映射δ:u→u,满足对任意的U,V,W∈u且UV=UW=0(或U·V=U·W=0),有δ([[U,V],W])=[[δ(U),V],W]+[[U,δ(V)],W]+[[U,V],δ(W)],则对任意U∈u,δ(U)=φ(U)+h(U),其中φ:u→u是一个导子,线性映射h:u→Z(u),满足对任意的U,V,W∈u且UV=UW=0(或U·V=U·W=0),有h([[U,V],W])=0. 相似文献
19.
We use computer algebra to determine all the multilinear polynomial identities of degree ≤7 satisfied by the trilinear operations (a·b)·c and a·(b·c) in the free dendriform dialgebra, where a·b is the pre-Lie or the pre-Jordan product. For the pre-Lie triple products, we obtain one identity in degree 3, and three independent identities in degree 5, and we show that every identity in degree 7 follows from the identities of lower degree. For the pre-Jordan triple products, there are no identities in degree 3, five independent identities in degree 5, and ten independent irreducible identities in degree 7. Our methods involve linear algebra on large matrices over finite fields, and the representation theory of the symmetric group. 相似文献
20.
Hader A. Elgendy 《代数通讯》2013,41(4):1785-1810
We construct universal associative envelopes for the nonassociative triple systems arising from the trilinear operations of Bremner and Peresi applied to the 2-dimensional simple associative triple system. We use noncommutative Gröbner bases to determine monomial bases, structure constants, and centers of the universal envelopes. We show that the infinite dimensional envelopes are closely related to the down-up algebras of Benkart and Roby. For the finite dimensional envelopes, we determine the Wedderburn decompositions and classify the irreducible representations. 相似文献