On the Derivations of Filiform Leibniz Algebras

The algebras of derivations of naturally graded Leibniz algebras are described. The existence of characteristically nilpotent Leibniz algebras in any dimension greater than 4 is proved.__________Translated from Matematicheskie Zametki, vol. 77, no. 5, 2005, pp. 733–742.Original Russian Text Copyright ©2005 by B. A. Omirov.     

Structure of Degenerate Block Algebras

Given a non-trivial torsion-free abelian group (A,+,Q), a field F of characteristic 0, and a non-degenerate bi-additive skew-symmetric map : A A F, we define a Lie algebra = (A, ) over F with basis {e_x | x A/{0}} and Lie product [e_x,e_y] = (x,y)e_x+y. We show that is endowed uniquely with a non-degenerate symmetric invariant bilinear form and the derivation algebra Der of is a complete Lie algebra. We describe the double extension D( , T) of by T, where T is spanned by the locally finite derivations of , and determine the second cohomology group H²(D( , T),F) using anti-derivations related to the form on D( , T). Finally, we compute the second Leibniz cohomology groups HL²( , F) and HL²(D( , T), F).2000 Mathematics Subject Classification: 17B05, 17B30This work was supported by the NNSF of China (19971044), the Doctoral Programme Foundation of Institution of Higher Education (97005511), and the Foundation of Jiangsu Educational Committee.     

A Five-term Exact Sequence for Opext of Crossed Modules in Lie Algebras

Extensions of crossed modules in Lie algebras with abelian kernel are studied, particularly backward and forward induced extensions and related properties. The set Opext((U, Q, ), (R, K, )) of congruence classes of extensions of (R, K, ) by (U, Q, ) is endowed with a K-vector space structure. This K-vector space appears in a five-term natural and exact sequence associated with an extension of crossed modules.2000 Mathematics Subject Classification: 17B56, 17B99, 18G99     

例谈中值定理应用中辅助函数的引入

通过实例分析，探讨在中值定理应用、中如何构造辅助函数的问题，以求开阔学生在面对此类问题时的解题思路．     

对甲氧基苯磺酰氯柱前衍生测定尿中游离羟脯氨酸与脯氨酸

以对甲氧基苯磺酰氯为衍生试剂,建立了分离测定人尿中游离羟脯氨酸和脯氨酸的高效液相色谱方法。考察了衍生温度、衍生缓冲液pH值、衍生时间、衍生剂用量对衍生反应的影响以及流动相组成、流动相缓冲液浓度、pH值和柱温对分离的影响。在优化条件下,羟脯氨酸和脯氨酸分别在5～100μmol/L和5～250μmol/L范围内呈良好线性,相关系数分别为0.999 4、0.999 5,检出限(S/N=3)分别为0.50 nmol/L和0.20 nmol/L,回收率(n=5)分别为95%～99%和96%～102%,相对标准偏差分别为2.1%～4.3%和2.0%～4.8%。该方法可用于人尿中游离羟脯氨酸和脯氨酸的定性定量分析。     

Cartan型模李超代数S(m,n;t)的中心扩张

本文研究了特征为素数p>2的有限维Special李超代数S(m,n;t)的中心扩张.通过计算从S(m,n;t)到S(m,n;t)^*的斜外导子,得到二阶上同调群H²(S(m,n;t),F)是平凡的.应用此结果,可得S(m,n;t)的中心扩张是平凡的.     

The Even Part of Finite-Dimensional Modular Lie Superalgebra Г

Let F be the underlying base field of characteristic p ＞ 3 and denote by Γō the even part of the finite-dimensional Lie superalgebra Γ.We give the generator sets of the Lie algebra Γō.Using certain properties of the canonical tori of Γō,we describe explicitly the derivation algebra of Γō.     

A note on envelopes of homotopies

In this article, we deal with the notion of the envelopes of homotopies which is the generalized version of functional envelopes in discrete dynamical systems. We prove the stability for envelopes of homotopies in complete normed algebra and we get the stabilities of the derivation and the extended derivation for the notion in the spaces.