共查询到20条相似文献，搜索用时 15 毫秒
1.
Antonio Giambruno Amitai Regev Michail V. Zaicev 《Transactions of the American Mathematical Society》2000,352(4):1935-1946
We study the exponential growth of the codimensions of a finite dimensional Lie algebra over a field of characteristic zero. In the case when is semisimple we show that exists and, when is algebraically closed, is equal to the dimension of the largest simple summand of . As a result we characterize central-simplicity: is central simple if and only if .
2.
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
3.
Antonio Fernández López 《代数通讯》2017,45(4):1577-1583
In a recent paper by the author and Golubkov, it was proved that a strongly prime Lie PI-algebra with an algebraic adjoint representation over an algebraically closed field of characteristic 0 is simple and finite dimensional. In this note, we derive this result from a more general one on strongly prime Lie PI-algebras with abelian minimal inner ideals, which is closely related to the intrinsic characterization of simple finitary Lie algebras with abelian minimal inner ideals. 相似文献
4.
Plamen Koshlukov 《代数通讯》2013,41(7):3095-3113
Let L be a Lie algebra, nilpotent of class 2, over an infinite field K, and suppose that the centre C of L is one dimensional; such Lie algebras are called Heisenberg algebras. Let ρ:L→hom KV be a finite dimensional representation of the Heisenberg algebra L such that ρ(C) contains non-singular linear transformations of V, and denote l(ρ) the ideal of identities for the representation ρ. We prove that the ideals of identities of representations containing I(ρ) and generated by multilinear polynomials satisfy the ACC. Let sl 2(L) be the Lie algebra of the traceless 2×2 matrices over K, and suppose the characteristic of K equals 2. As a corollary we obtain that the ideals of identities of representations of Lie algebras containing that of the regular representation of sl 2(K) and generated by multilinear polynomials, are finitely based. In addition we show that one cannot simply dispense with the condition of multilinearity. Namely, we show that the ACC is violated for the ideals of representations of Lie algebras (over an infinite field of characteristic 2) that contain the identities of the regular representation of sl 2(K). 相似文献
5.
7.
8.
9.
Askar Dzhumadil’daev 《代数通讯》2018,46(1):129-142
We prove that assosymmetric algebras under the Jordan product are Lie triple algebras. A Lie triple algebra is called special if it is isomorphic to a subalgebra of the plus-algebra of some assosymmetric algebra. We establish that the Glennie identity of degree 8 is valid for special Lie triple algebras, but not for all Lie triple algebras. 相似文献
10.
Said Benayadi 《Proceedings of the American Mathematical Society》1997,125(3):685-688
Using Casimir elements, we characterize the semisimple Lie algebras among the quadratic Lie algebras. This characterization gives, in particular, a generalization of a consequence of Cartan's second criterion.
11.
Murray R. Bremner 《Linear and Multilinear Algebra》2013,61(12):1671-1682
We use computer algebra to demonstrate the existence of a multilinear polynomial identity of degree 8 satisfied by the bilinear operation in every Lie–Yamaguti algebra. This identity is a consequence of the defining identities for Lie–Yamaguti algebras, but is not a consequence of anticommutativity. We give an explicit form of this identity as an alternating sum over all permutations of the variables in a nonassociative polynomial with 8 terms. Our computations show that no such identities exist in degrees less than 8. 相似文献
12.
Ivan Kaygorodov Alexander Pozhidaev Paulo Saraiva 《Linear and Multilinear Algebra》2019,67(6):1074-1102
13.
14.
Wen-Xiu Ma 《Applied mathematics and computation》2011,217(17):7238-7244
Based on a kind of special non-semisimple Lie algebras, a scheme is presented for constructing nonlinear continuous integrable couplings. Variational identities over the corresponding loop algebras are used to furnish Hamiltonian structures for the resulting continuous integrable couplings. The application of the scheme is illustrated by an example of nonlinear continuous integrable Hamiltonian couplings of the AKNS hierarchy of soliton equations. 相似文献
15.
Fangyan Lu 《Mathematische Nachrichten》2007,280(8):882-887
Let δ be a Lie triple derivation from a nest algebra ?? into an ??‐bimodule ??. We show that if ?? is a weak* closed operator algebra containing ?? then there are an element S ∈ ?? and a linear functional f on ?? such that δ (A) = SA – AS + f (A)I for all A ∈ ??, and if ?? is the ideal of all compact operators then there is a compact operator K such that δ (A) = KA – AK for all A ∈ ??. As applications, Lie derivations and Jordan derivations on nest algebras are characterized. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
16.
《代数通讯》2013,41(9):4267-4275
Abstract In Fortes (2001), we introduced a notion of order for associative pairs and we obtained a Goldie-like characterization of left orders in a semiprime pair coinciding with its socle. In this paper, we take up again that notion of order to establish a Faith-Utumi theorem, which studies left orders in a prime pair coinciding with its socle. 相似文献
17.
《代数通讯》2013,41(9):3487-3501
Abstract Let A be a semiprime associative algebra with an involution over a field of characteristic not 2, let K be the Lie algebra of all skew elements of A, and let Z [K, K] denote the annihilator of the Lie algebra [K, K]. We will prove that the multiplication algebra of the semiprime Lie algebra [K, K]/Z [K, K] is also semiprime. As a consequence, the multiplication algebra of [K, K]/Z [K, K] is prime, whenever [K, K]/Z [K, K] is prime. We will obtain similar results for the Lie algebra K/Z K whenever the base field has characteristic zero. 相似文献
18.
19.
20.
We investigate the properties of bounded operators which satisfy a certain spectral additivity condition, and use our results to study Lie and Jordan algebras of compact operators. We prove that these algebras have nontrivial invariant subspaces when their elements have sublinear or submultiplicative spectrum, and when they satisfy simple trace conditions. In certain cases we show that these conditions imply that the algebra is (simultaneously) triangularizable. 相似文献