Yufang Zhao, Yongsheng Cheng
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.
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Cohomological rigidity of conformal Galilei algebras and their central extensions
本文研究实共形伽利略代数复化及其中心扩张的第二伴随上同调，利用霍赫希尔德-塞尔分解定理计算相关空间，得出自旋为半整数时d≠2的共形伽利略代数具上同调刚性的结论，完成特定参数范围的形式刚性刻画。
Local Derivations on Conformal Galilei Algebras and Their Central Extensions
本文统一研究了共形伽利略代数在三种中心扩张情形下的局部导子，确定了其结构，并解决了代数自反性问题，揭示了质量中心扩张消除额外局部自由度的关键作用。
In this paper, we introduce the notion of BiHom-Lie conformal superalgebras. We develop its representation theory and define the cohomology group with coefficients in a module. Finally, we introduce conformal derivations of BiHom-Lie conformal superalgebras and study some of their properties.
In this paper, we focus on the $(\si,\t)$-derivation theory of Lie conformal superalgebras. Firstly, we study the fundamental properties of conformal $(\si,\t)$-derivations. Secondly, we mainly research the interiors of conformal $G$-derivations. Finally, we discuss the relationships between the conformal $(\si,\t)$-derivations and some generalized conformal derivations of Lie conformal superalgebras.
We characterise Lie groups with bi-invariant bargmannian, galilean or carrollian structures. Localising at the identity, we show that Lie algebras with ad-invariant bargmannian, carrollian or galilean structures are actually determined by the same data: a metric Lie algebra with a skew-symmetric derivation. This is the same data defining a one-dimensional double extension of the metric Lie algebra and, indeed, bargmannian Lie algebras coincide with such double extensions, containing carrollian Lie algebras as an ideal and projecting to galilean Lie algebras. This sets up a canonical correspond…
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.
Deformations and generalized derivations of Lie conformal superalgebras
将经典李共形代数的上同调理论和共形导子理论推广到李共形超代数。首先，我们构造了李共形超代数及其共形模的半直积，并研究了这种半直积的导子。其次，我们发展了李共形超代数的上同调理论，并讨论了它在李共形超代数形变研究中的应用。最后，我们引入了李共形超代数的广义导子并研究了它们的性质。
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。
Deformations and generalized derivations of Hom-Lie conformal algebras
将经典共形李代数的上同调理论和共形导子理论推广到Hom-Lie共形代数。本文发展了Hom-李共形代数的上同调理论，并讨论了它在正则Hom-李共形代数变形研究中的应用。同时，我们还引入了乘法Hom-Lie共形代数的$α^k$ -导子，并研究了它们的性质。
Conformal triple derivations and triple homomorphisms of Lie conformal algebras
本文研究有限李共形代数的共形三重导子代数，给出有限单李共形代数上（广义）共形三重导子代数的完整分类，并引入并刻画了三重同态。
On some derivations of Lie conformal superalgebras
本文研究 Lie 共形超代数上的共形导子、三重导子及广义情形，完成有限单情形分类，并引入 $(A,B,C,D)$-导子与三重同态。
Representations and derivations of Hom-Lie conformal superalgebras
本文引入了Hom-Lie共形超代数的表示论，并讨论了伴随表示的情形。进一步发展了Hom-Lie共形超代数的上同调理论，并讨论了它在正则Hom-Lie共形超代数形变研究中的应用。最后，我们引入了乘法Hom-Lie共形超代数的导子并研究了它们的性质。
Cohomology and derivations of BiHom-Lie conformal algebras
本文引入了BiHom-Lie共形代数的概念，并发展了它的上同调理论。同时，我们还讨论了它在正则BiHom-李共形代数变形研究中的一些应用。最后，我们引入了乘法BiHom-Lie共形代数的导子并研究了它们的性质。
A quadratic Lie conformal algebra corresponds to a Hamiltonian pair in \cite{GD}, which plays fundamental roles in completely integrable systems. Moreover, it also corresponds to certain compatible pairs of a Lie algebra and a Novikov algebra which was called Gel'fand-Dorfman bialgebra by Xu in \cite{X1}. In this paper, central extensions and conformal derivations of quadratic Lie conformal algebras are studied in terms of Gel'fand-Dorfman bialgebras. It is shown that central extensions and conformal derivations of a quadratic Lie conformal algebra are related with some bilinear forms and some…
Transposed Poisson Structures on the planar Galilean conformal algebra
本研究证明平面伽利略共形代数的所有1/2-导子均为标量，进而得出该代数上的所有转置泊松结构都是平凡的结论。
Let $p$ be a nonzero complex number. Recently, a class of infinite rank Lie conformal algebras $\mathfrak{B}(p)$ was introduced in [13]. In this paper, we study the structure theory of this class of Lie conformal algebras. Specifically, we completely determine the conformal derivations, the conformal biderivations and certain second cohomologies of $\mathfrak{B}(p)$.
A Lie conformal algebra of Block type
本文的目的是研究Block型李共形代数。本文研究了Block型共形李代数的共形导子、秩为1的共形模和低维共形。构造了与Block型共形李代数相关联的顶点Poisson代数结构。
A new class of Z-graded Lie conformal algebras of infinite rank
本文构造了一类新的无限秩$\Z$ -分次共形李代数$\CW(a,c)$.完全确定了$\CW(a,c)$的共形导子和一维中心扩张。证明了$\CW(a,c) (a\neq0)$上秩为1的共形模是平凡的，并对$\CW(0,c)$上秩为1的非平凡（不可约）模进行了分类.
Structures of $W(2,2)$ Lie conformal algebra
研究了具有自由$\mathbb{C}[\partial]$基$\{L, M\}$的$W(2,2)$李共形代数，使得$[L_λL]=(\partial+2λ)L$，$[L_λM]=(\partial+2λ)M$，$[M_λM]=0$ .本文研究了这类共形李代数的共形导子、中心扩张和共形模。此外，我们还计算了这个李共形代数的模中含有系数的上同调。特别是，我们确定其上同调与平凡系数的基本和减少复杂。
On Schrödinger-Virasoro type Lie conformal algebras
本文对a，b，cPDMATHABMM \mathbb{C}引入了两类新的非单Schrödinger-Virasoro型共形李代数TSV（a，b）和TSV（c）.此外，还确定了TSV（a，b）和TSV（c）的秩为1的中心扩张、共形导子和自由共形模.
Differential envelopes of Novikov conformal algebras
研究Novikov conformal代数的微分包络性质，证明有限生成代数可嵌入可交换代数，但无限生成代数不成立。
In this paper, we introduce the representation theory of $δ$-Hom-Jordan Lie conformal superalgebras and discuss the cases of adjoint representations. Furthermore, we develop the cohomology theory of Hom-Lie conformal superalgebras and discuss some applications to the study of deformations of regular $δ$-Hom-Jordan Lie conformal superalgebras. Finally, we introduce derivations of multiplicative $δ$-Hom-Jordan Lie conformal superalgebras and study their properties.
Infinite rank Schrodinger-Virasoro type Lie conformal algebras
受Loop Virasoro李共形代数上某些模的结构和Schrodinger-Virasoro代数的李结构的启发，构造了一类无限秩李共形代数CSV（a，b），其中a，b为复数.一致确定了CSV（a，b）的共形导子.对CSV（a，b）上的秩1共形模和Z-分次自由中间级数模进行了分类.给出了CSV（a，b）的共形子代数CHV（a，b）的相应结果.
Jacobi-Jordan conformal algebras: Basics, Constructions and related structures
本文引入并研究了 Jacobi-Jordan conformal algebra 的概念，探讨了其共形模、表示、O-算子、共形导子、二次结构及统一积，并通过构造上同调对象为 C[delta]-split extending structures problem 提供了理论解答。
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