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1.
S. Mattarei 《Israel Journal of Mathematics》2007,160(1):23-40
Nonsingular derivations of modular Lie algebras which have finite multiplicative order play a role in the coclass theory for
pro-p groups and Lie algebras. A study of the set
of positive integers which occur as orders of nonsingular derivations of finite-dimensional nonnilpotent Lie algebras of
characteristic p > 0 was initiated by Shalev and continued by the present author. In this paper we continue this study in the case of characteristic
two. Among other results, we prove that any divisor n of 2k − 1 with n
4 > (2k − n)3 belongs to
. Our methods consist of elementary arguments with polynomials over finite fields and a little character theory of finite
groups.
This work was partially supported by Ministero dell’Istruzione e dell’Università, Italy, through PRIN “Graded Lie algebras
and pro-p-groups of finite width”. 相似文献
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In this paper some new results on analytic domination of operators and on integrability of Lie algebras of operators are proved and then our methods are applied to the study of Lie algebras of unbounded derivations in algebras. 相似文献
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In this paper we prove that every nonlinear Lie derivation of triangular algebras is the sum of an additive derivation and a map into its center sending commutators to zero. 相似文献
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Fangyan Lu 《Israel Journal of Mathematics》2006,155(1):149-156
It is shown that each Lie derivation on a reflexive algebra, whose lattice is completely distributive and commutative, can
be uniquely decomposed into the sum of a derivation and a linear mapping with image in the center of the algebra.
Supported by NNSFC (No. 10571054) and a grant (No.04KJB110116) from the government of Jiangsu Province of China. 相似文献
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Generalized Lie derivations on triangular algebras 总被引:1,自引:0,他引:1
Dominik Benkovi? 《Linear algebra and its applications》2011,434(6):1532-1544
Let A be a unital algebra and let M be a unitary A-bimodule. We consider generalized Lie derivations mapping from A to M. Our results are applied to triangular algebras, in particular to nest algebras and (block) upper triangular matrix algebras. We prove that under certain conditions each generalized Lie derivation of a triangular algebra A is the sum of a generalized derivation and a central map which vanishes on all commutators of A. 相似文献
8.
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
9.
LetF be a commutative ring with 1, letA, be a primeF-algebra with Martindale extended centroidC and with central closureA
c
and letR be a noncentral Lie ideal of the algebraA generatingA. Further, letZ(R) be the center ofR, let
be the factor Lie algebra and let δ:
be a Lie derivation. Suppose that char(A) ≠ 2 andA does not satisfySt
14, the standard identity of degree 14. We show thatR ΩC =Z(R) and there exists a derivation of algebrasD:A →A
c
such that
for allx∈R. Our result solves an old problem of Herstein. 相似文献
10.
Let T be a triangular algebra over a commutative ring R. In this paper, under some mild conditions on T, we prove that if δ:T→T is an R-linear map satisfying
δ([x,y])=[δ(x),y]+[x,δ(y)] 相似文献
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Ping-Bao Liao 《Linear algebra and its applications》2009,430(4):1236-197
Let A be a prime algebra of characteristic not 2 with extended centroid C, let R be a noncentral Lie ideal of A and let B be the subalgebra of A generated by R. If f,d:R→A are linear maps satisfying that
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Rolf Farnstein 《Mathematische Annalen》1990,288(1):713-730
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Xiao Fei Qi 《数学学报(英文版)》2013,29(5):1007-1018
Let $\mathcal{A}$ and $\mathcal{B}$ be unital rings, and $\mathcal{M}$ be an $\left( {\mathcal{A},\mathcal{B}} \right)$ -bimodule, which is faithful as a left $\mathcal{A}$ -module and also as a right $\mathcal{B}$ -module. Let $\mathcal{U} = Tri\left( {\mathcal{A},\mathcal{M},\mathcal{B}} \right)$ be the triangular algebra. In this paper, we give some different characterizations of Lie higher derivations on $\mathcal{U}$ . 相似文献