Derivations of Group Algebras
A. A. Arutyunov, A. S. Mishchenko, A. I. Shtern
给出了可表示群的群代数的外导子的一种刻划方法。利用群的伴随作用的广群的特征刻划导子。
In the paper, a method of describing the outer derivations of the group algebra of a finitely presentable group is given. The description of derivations is given in terms of characters of the groupoid of the adjoint action of the group.
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We investigate the action of Schur algebra on the Lie algebras of derivations of free Lie algebras and operad structures constructed from it. We also show that the Lie algebra of derivations is generated by quadratic derivations together with the action of the Schur operad. Applications to certain subgroups of the automorphism group of a finitely generated free group are given as well.
Lie Higher Derivations on Generalized Matrix Algebras
本文首先刻画了广义矩阵代数上的李高导子和高导子的构造，然后给出了广义矩阵代数上的李高导子是适当的条件.最后，讨论了研究结果的应用。
Derivations of Leavitt path algebra
本文描述了具有单位的结合交换环$K$中系数为行有限的图$Γ$的Leavitt路代数$L_K(Γ)$的外导子的$K$ -模$HH^1(L_K(Γ))$.我们给出了$L_K(Γ)$的每一个外导子的一个显式公式。我们还描述了Toeplitz代数的外导子的李代数结构，并证明了Leavitt路代数的每个导子都可以扩张为相应的$C^*$ -代数的导子.
Genetic Volterra algebras and their derivations
本文主要研究遗传Volterra代数。我们首先研究这类代数的特征。我们充分描述联想遗传Volterra代数，在这种情况下，所有的导子是平凡的。在一般情况下，即当代数不是结合代数时，我们给出了一般Volterra代数上平凡导子的一个充分条件.此外，我们描述了所有导子的三维一般Volterra代数，这使我们能够证明，任何局部导子是一个导子的代数。
Left-symmetric algebras of derivations of free algebras
引入了一个左对称代数在一个自由代数的所有导子集合上的结构，使得它的换位子代数成为导子的通常李代数.研究导子左对称代数的左、右幂零元。给出了导子的单左对称代数和导子的Novikov代数.证明了单自由变元的自由非结合对称$m$ -元代数的导子的左对称代数的正部分是由一个导子生成的，并刻画了某些右幂零导子.
Jordan Derivations of some extension algebras
本文主要研究了对偶扩张代数和广义单点扩张代数的Jordan导子。证明了对偶扩张代数的每个Jordan导子都是导子。作为应用，我们得到了对偶扩张代数上的每个Jordan广义导子和每个广义Jordan导子都是广义导子。对于广义单点扩张代数，证明了在一定条件下，它们的每个Jordan导子都是导子与反导子之和。
Derivations of the Leavitt path algebra W(n)
给出了Leavitt路代数W（n）的全部内导子和全部外导子的显式描述.事实上，已经描述了Leavitt路代数W（n）的所有内导子和所有外导子的空间。
(n+1)-Ary derivations of simple Malcev algebras
定义了n元代数的（n +1）元导子。本文描述了单Malcev代数的3-导子和单三元Malcev代数M_8的4-元导子。
N-derivations for finitely generated graded Lie algebras
$N$ -导子是导子和三元导子的自然推广。设${\cal L}$是由有限维Cartan子代数分次生成的李代数.本文给出了${\cal L}$的Lie $N$ -导子代数与${\cal L}$的Lie导子代数重合的一个充分条件.作为应用，Schrödinger-Virasoro代数、广义Witt代数、Kac-Moody代数及其Borel子代数的任何$N$ -导子都是导子.
The concept of derivation for Lie-Yamaguti algebras is generalized in this paper. A quasi-derivation of an LY-algebra is embedded as derivation in a larger LY-algebra. The relationship between quasi-derivations and robustness of Lie-Yamaguti algebras has been studied.
Alternative algebras admitting derivations with invertible values and invertible derivations
本文描述了所有导子可逆的交错代数（类似于Bergen-Herstein-Lanski定理），并证明了类似于Moens定理.
Derivations and 2-local derivations on the mirror Heisenberg-Virasoro algebra
本文利用第一上同调确定了镜像Heisenberg-Virasoro代数上的导子，并进一步证明该代数上的任意2-局部导子均为导子。
We show that in the class of solvable Lie algebras there exist algebras which admit local derivations which are not ordinary derivation and also algebras for which every local derivation is a derivation. We found necessary and sufficient conditions under which any local derivation of solvable Lie algebras with abelian nilradical and one-dimensional complementary space is a derivation. Moreover, we prove that every local derivation on a finite-dimensional solvable Lie algebra with model nilradical and maximal dimension of complementary space is a derivation.
Jordan Derivations and Lie derivations on Path Algebras
在不作忠实假设的情况下，证明了一类无定向圈箭图路代数上的每一Jordan导子都是导子，且这类代数上的每一Lie导子都具有标准式.
On the abelianization of the special derivation Lie algebras of free Lie algebras
本文通过Morita迹证明自由李代数特殊导数李代数的交换化包含无限多个线性无关元素，并展示其中存在被Morita迹杀死的非平凡元素。
Derivations, Centroids and Iner-Derivations of $\textbf{5}$-Dimensional Nilpotent Complex Associative Algebras
本研究分析了5维复幂零结合代数的导子、中心化子和内导子，并给出了维数小于5的此类代数及其相关结构的分类。
The present paper is devoted to study 2-local derivations on W-algebra $W(2,2)$ which is an infinite-dimensional Lie algebras with some out derivations. We prove that all 2-local derivations on the W-algebra $W(2,2)$ are derivation. We also give a complete classification of the 2-local derivation on the so called thin Lie algebra and prove that it admits a lots of 2-local derivations which are not derivations.
Algebraic derivations and radicals of automorphism groups of algebras
本文研究半素结合代数的代数导子与相关自同构群的根性质，证明其素根与弱可解根重合，并联系Martindale商环内导子描述。
The derivation algebra and automorphism group of the twisted Schrödinger-Virasoro algebra
本文确定了扭Schrödinger-Virasoro代数的导子代数和自同构群.
We show that any local derivation on the solvable Leibniz algebras with model or abelian nilradicals, whose the dimension of complementary space is maximal is a derivation. We show that solvable Leibniz algebras with abelian nilradicals, which have 1-dimension complementary space, admit local derivations which are not derivations. Moreover, similar problem concerning 1-local derivations of such algebras are investigated and an example of solvable Leibniz algebra given such that any 2-local derivation on it is a derivation, but which admit local derivations which are not derivations.
The present paper is devoted to study 2-local derivations on infinite-dimensional Lie algebras over a field of characteristic zero. We prove that all 2-local derivations on the Witt algebra as well as on the positive Witt algebra are (global)derivations, and give an example of infinite-dimensional Lie algebra with a 2-local derivation which is not a derivation.
In the present paper, we prove that every local and $2$-local derivation of the complex finite-dimensional simple Filippov algebra is a derivation. As a corollary we have the description of all local and $2$-local derivations of complex finite-dimensional semisimple Filippov algebras. All local derivations of the ternary Malcev algebra $M_8$ are described. It is the first example of a finite-dimensional simple algebra that admits pure local derivations, i.e. algebra admits a local derivation which is not a derivation.
Sur les algèbres de Lie quasi-filiformes admettant un tore de dérivations [On quasi-filiform Lie algebras admitting a torus of derivations]
描述了非零秩的拟丝状李代数。修正了丝状和拟丝状自然分次代数代数的分类。
On Jordan Derivations of Triangular Algebras
本文证明了三角代数的每一个若当导子都是导子。
Lie algebras of triangular polynomial derivations and an isomorphism criterion for their Lie factor algebras
对单三角多项式导子的李代数的理想进行了分类。给出了单三角多项式导子的李代数的李因子代数的同构准则。
We investigate almost inner derivations of some finite-dimensional nilpotent Leibniz algebras. We show the existence of almost inner derivations of Leibniz filiform non-Lie algebras differing from inner derivations, we also show that the almost inner derivations of some filiform Leibniz algebras containing filiform Lie algebras do not coincide with inner derivations.
Local derivations on finite-dimensional Lie algebras
证明了特征为零的代数闭域上的有限维半单李代数上的每一个局部导子都是导子。我们还给出了有限维幂零李代数$\mathcal{L}$与$\dim\mathcal{L}\geq 3$的例子，其中允许局部导子不是导子。
In this paper, we first study derivations in non nilpotent Lie triple algebras. We determine the structure of derivation algebra according to whether the algebra admits an idempotent or a pseudo-idempotent. We study the multiplicative structure of non nilpotent dimensionally nilpotent Lie triple algebras. We show that when $n=2p+1$ the adapted basis coincides with the canonical basis of the gametic algebra $G(2p+2,2)$ or this one obviously associated to a pseudo-idempotent and if $n=2p$ then the algebra is either one of the precedent case or a conservative Bernstein algebra.
(n+1)-Ary derivations os semisimple Filippov algebras
定义了$n$ -元代数的（n+1）-元导子.研究了有限维单和半单Filippov代数在代数闭域零特征上的（n+1）-导子.我们构造了Filippov代数的非平凡（n+1）元导子的新例子。
We investigate generalized derivations of $n$-BiHom-Lie algebras. We introduce and study properties of derivations, $( α^{s},β^{r}) $-derivations and generalized derivations. We also study quasiderivations of $n$-BiHom-Lie algebras. Generalized derivations of $(n+1)$-BiHom-Lie algebras induced by $ n $-BiHom-Lie algebras are also considered.
The present paper is devoted to studying 2-local derivations on the planar Galilean conformal algebra. We prove that every 2-local derivation on the planar Galilean conformal algebra is a derivation.
On the algebra of derivations of some low-dimensional Leibniz algebras
本文考察若干低维幂零 Leibniz 代数，重点研究其导子代数的代数结构。
Generalized conformal derivations of Lie conformal algebras
设$R$是李共形代数.本文研究了共形导子代数$CDer(R)$、共形拟导子代数$QDer(R)$和广义共形导子代数$GDer(R)$ .广义共形导子代数代数是共形导子代数代数的自然推广。显然，我们有下面的塔$CDer(R)\subseteq QDer(R)\subseteq GDer(R)\subseteq gc(R)$，其中$gc(R)$是一般的李共形代数。此外，我们主要研究了这些广义共形导子之间的联系。最后，研究了共形李代数的共形$(α,β,γ)$ -导子。此外，我们还得到了几个具体的广义共形导子与共形$(α,β,γ)$ -导子之间的联系。此外，还刻画了有限单共形李代数的所有共形$(α,β,γ)$ -导子。
2-local derivation is a generalized derivation for a Lie algebra, which plays an important role to the study of local properties of the structure of the Lie algebra. In this paper, we prove that every 2-local derivation on the conformal Galilei algebra is a derivation.
2-Local derivations on a Block-type Lie algebra
本文研究了块型李代数上的2-局部导数，证明其本质上为导数。
Local super-derivations of the super Schrödinger algebras
本文研究了超Schrödinger代数的局部超导子，并证明了其上的每个局部超导子均为超导子。
In this paper, we describe all derivations on four dimensional genetic Volterra algebras. We show that any local derivation is a derivation of the algebra. It is a positive answer to a conjecture made by Ganikhodzhaev, Mukhamedov, Pirnapasov and Qaralleh.
In the paper we give a complete classification of $2$-dimensional evolution algebras over algebraically closed fields, describe their groups of automorphisms and derivation algebras.
In the present paper we study local and 2-local derivations of locally finite split simple Lie algebras. Namely, we show that every local and 2-local derivation on such Lie algebra is a derivation.
2-local derivation is a generalized derivation for a Lie algebra, which plays an important role to the study of local properties of the structure of the Lie algebra. In this paper, we prove that every 2-local derivation on the twisted Heisenberg-Virasoro algebra is a derivation.
Nonlinear Jordan Derivations of Triangular Algebras
本文证明了三角代数上的任何非线性Jordan导子都是可加导子。作为副产品，我们得到了无限维希尔伯特空间上套代数上的任何非线性Jordan导子都是内导子。
$δ$-derivations of n-ary algebras
本文研究n元Filippov代数的$δ$-导子，给出其描述，得到特征零代数闭域上单有限维Filippov代数的相关结果，给出非平凡$δ$-导子新例子，证明单三元Malcev代数$M_8$无此类导子。
Derivation double Lie algebras
研究了李代数L的经典R-矩阵D，使得D也是L的导子。这就产生了导子双李代数（L，D）.动机来自最近的工作后李代数结构对李代数产生的研究中的零仿射行动的李群。证明了不存在非平凡单导子双李代数，并研究了任意李代数的相关李代数恒等式。
Generalized derivations of (color) n-ary algebras
本文将Leger和Luks关于李代数的广义导子的结果推广到色$n$ -元$Ω$ -代数的情形.特别地，我们证明了色$n$ -代数的广义导子的一些性质，证明了色$n$-代数的拟导子代数可以嵌入到更大的色$n$-代数的导子代数中，并描述了满足条件$QDer = End.$的（反）交换$n$-代数
The automorphisms groups and derivation algebras of all two-dimensional algebras over algebraically closed fields are described.
Derivations and local derivations on Euclidean Lie algebras
本文研究欧几里得李代数 e(n) 的导子和局部导子，给出了 n≥4 时导子代数的完整描述，并证明了 e(n) 上的每个局部导子都是导子。
Derivation algebras and automorphism groups of a class of deformative super $W$-algebras $W^s_λ(2,2)$
本文确定了一类变形超$W$ -代数$W_λ(2,2)$的导子代数和自同构群。
$δ$-derivations of semisimple finite-dimensional structurable algebras
本文在特征非2、3、5的代数闭域上，证明半单有限维可构造代数无任何非平凡δ-导子。
Let C be a commutative ring with unity. In this article, we show that every Jordan derivation over an upper triangular matrix algebra T_n(C) is an inner derivation. Further, we extend the result for Jordan derivation on full matrix algebra M_n(C).
In this paper, we prove that every 2-local derivation on Witt algebras $W_n, W_n^+$ or $W_n^{++} $ is a derivation for all $n=1,2,\cdots,\infty$. As a consequence we obtain that every 2-local derivation on any centerless generalized Virasoro algebra of higher rank is a derivation.
The derivation algebra and automorphism group of the (generalized) twisted N=2 superconformal algebra
本文确定了扭N=2超共形代数的导子代数和自同构群。最后，我们将相关结果推广到广义扭N=2超共形代数。
The Derivation algebra and automorphism group of the generalized Ramond N=2 superconformal algebra
给出了广义Ramond N=2超共形代数的定义，讨论了广义Ramond N=2超共形代数的导子代数和自同构群
Local And 2-Local Derivations On Algebras Of Measurable Operators
本文综述了vonNeumann代数中各种可测算子代数上的导子、局部导子和2-局部导子的最新研究结果。除了von Neumann代数是II型$_1$的情况外，我们给出了这些代数上导子的完整描述.在后一种情况下，该结果是在导子的测度连续的一个额外条件下得到的。还考虑了上述代数上的局部导子和2-局部导子。给出了von Neumann代数$M$上隶属于$M$的可测算子代数上的每一个局部或2-局部导子自动成为导子的充分条件.我们还给出了可测算子的交换代数的例子，允许局部和2-局部导子不是导子。
In this paper, we give some construction about ternary Jordan algebras at first. Next we study relationships between generalized derivations, quasiderivations and centroids of ternary Jordan algebras. We show that for ternary Jordan algebras, generalized derivation algebras are the sum of quasiderivation algebras and centroids where centroids are ideals of generalized derivation algebras. We also prove that quasiderivations can be embedded into larger ternary Jordan algebras as derivations. In particular, we also determine dimensions of ternary Jordan algebras in the case of all linear transfo…
We describe automorphisms and derivations of several important associative and Lie algebras of infinite matrices over a field.
Derivation Algebras of Centerless Perfect Lie Algebras Are Complete
证明了任意特征域上任意维数的无中心完美李代数的导子代数代数是完备的，无中心完美李代数的全形是完备的当且仅当它的外导子代数代数是无中心的.
We study endomorphisms and derivations of infinite dimensional cyclic Leibniz algebra.
Local and 2-local derivations and automorphisms on simple Leibniz algebras
本文研究了复有限维单Leibniz代数的局部导子和2-局部导子及自同构。证明了有限维复单Leibniz代数上的所有局部导子和2-局部导子都是自动导子。我们证明了幂零Leibniz代数作为一个规则，允许局部导子和2-局部导子不是导子。进一步考虑了单Leibniz代数的自同构。证明了复有限维单Leibniz代数上的2-局部自同构是自同构，并证明了幂零Leibniz代数允许非自同构的2-局部自同构.将单Leibniz代数上的局部自同构的一个类似问题归结为单李代数的情形。
Derivations, 2-local derivations, biderivations and automorphisms of generalized Loop Heisenberg-Virasoro algebras
本文引入广义Loop Heisenberg-Virasoro代数，确定其导子、证明2-局部导子为导子、双导子为内双导子并给出应用，最后给出自同构群。
Derivations and 2-Cocycles of Contact Lie Algebras Related to Locally-Finite Derivations
经典切触李代数是经典力学中位形空间切触元流形上的基本代数结构。徐介绍了接触单李代数，这是有关的局部有限导子和一般不分次的大类。这些李代数的同构类在以前的论文中确定的徐和苏。本文确定了这类李代数的导子代数代数和2-上同调群，并得到了这类李代数的2-上同调群都是平凡的。
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