Extensions of super Lie algebras
Dmitri Alekseevsky, Peter W. Michor, Wolfgang Ruppert
我们研究了一个给定的超李代数的（非交换）扩张，确定了一个上同调障碍的存在性，平行于已知的李代数。类比设置协变的外部衍生物，曲率，和微分几何中的比安奇身份的阐述。
We study (non-abelian) extensions of a given super Lie algebra, identify a cohomological obstruction to the existence, parallel to the known one for Lie algebras. An analogy to the setting of covariant exterior derivatives, curvature, and the Bianchi identity in differential geometry is spelled out.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
继续探索
We calculate the first extension groups for finite-dimensional simple modules over an arbitrary generalized current Lie algebra, which includes the case of loop Lie algebras and their multivariable analogs.
We study the central extensions of Lie algebras graded by an irreducible locally finite root system.
In this note we show that the theory of non abelian extensions of a Lie algebra $\mathfrak{g}$ by a Lie algebra $\mathfrak{h}$ can be understood in terms of a differential graded Lie algebra $L$. More precisely we show that the non-abelian cohomology $H^2_{nab}(\mathfrak{g},\mathfrak{h})$ is $\mathcal{MC}(L)$, the $π_0$ of the Deligne groupoid of $L$.
Cohomology, Extensions and Deformations of restricted Lie triple systems
本文构建了受限李三系的低阶上同调理论，定义了直到5阶的受限上链与上边界算子，并阐释了低阶上同调群在导子、模扩张、形式形变及系统扩张中的代数意义。
In this paper we study (non-Abelian) extensions of a given hom-Lie color algebra and provide a geometrical interpretation of extensions. In particular, we characterize an extension of a hom-Lie algebra $\mathfrak{g}$ by another hom-Lie algebra $\mathfrak{h}$ and we discuss the case where $\mathfrak{h}$ has no center. We also deal with the setting of covariant exterior derivatives, Chevalley derivative, curvature and the Bianchi identity for the possible extensions in differential geometry. Moreover, we find a cohomological obstruction to the existence of extensions of hom-Lie color algebras, i…
Hopf Galois extensions, triangular structures, and Frobenius Lie algebras in prime characteristic
研究了变换霍普夫代数在HopfGalois扩张中的性质.本文的最终目的是引入特征域$p>0$上与限制Frobenius李代数相关的三角霍普夫代数.
From a Lie algebra $\mathfrak{g}$ satisfying $\mathcal{Z}(\mathfrak{g})=0$ and $Λ^2(\mathfrak{g})^\mathfrak{g}=0$ (in particular, for $\g$ semisimple) we describe explicitly all Lie bialgebra structures on extensions of the form $\mathfrak{L} =\mathfrak{g}\times \mathbb{K}$ in terms of Lie bialgebra structures on $\mathfrak{g}$ (not necessarily factorizable nor quasi-triangular) and its biderivations, for any field $\mathbb{K}$ with char $\mathbb{K}=0$. If moreover, $[\mathfrak{g},\mathfrak{g}]=\mathfrak{g}$, then we describe also all Lie bialgebra structures on extensions $\mathfrak{L} =\math…
The construction of HNN-extensions of involutive Hom-associative algebras and involutive Hom-Lie algebras is described. Then, as an application of HNN-extension, by using the validity of Poincaré-Birkhoff-Witt theorem for involutive Hom-Lie algebras, we provide an embedding theorem.
Module Extensions Over Classical Lie Superalgebras
我们研究了经典李超代数上不可分解的内射模的某些滤子，应用Brown，Jategaonkar，Lenagan和Warfield提出的诺特环的一般方法.为了说明我们分析的结果，假设$g$是一个复的经典单李超代数，并且$E$是一个不可分解的单射$g$ -模，其基座$L$非零（因此必然是单的）。（回想一下，$L$的每一个本质扩张，特别是$L$通过一个简单模的每一个非分裂扩张，都可以由$g$ -$E$的子因子形成。）将李代数理论直接转置到这种情况是不可能的。然而，我们能够提出一个有限上界，很容易计算和依赖于$g$，简单的最高权$g$ -模块出现的$g$ -子因子的$E$的同构类的数量。
Generalized quantization scheme for central extensions of Lie algebras
给出了在向量空间上求非线性Poisson-Lie群结构及其量子化的方法。对于李代数的任意中心扩张，给出了量子化的显式公式。
The Onsager Lie algebra $O$ is often used to study integrable lattice models. The universal enveloping algebra of $O$ admits a $q$-deformation $O_q$ called the $q$-Onsager algebra. Recently, an algebra $\mathcal O_q$ was introduced called the alternating central extension of $O_q$. In this paper we introduce a Lie algebra $\mathcal O$ that is roughly described by the following two analogies: (i) $\mathcal O$ is to $O$ as $\mathcal O_q$ is to $O_q$; (ii) $O_q$ is to $O$ as $\mathcal O_q$ is to $\mathcal O$. We call $\mathcal O$ the alternating central extension of $O$. This paper contains a com…
The purpose of this paper is to study Virasoro extensions of the q-deformed Witt Hom-Lie superalgebra. Moreover, we provide the cohomology and deformations of the Ramond Hom-superalgebra and special Ramond Hom-superalgebra.
In this paper we show that non abelian extensions of an associative algebra $\mathcal{B}$ by an associative algebra $\mathcal{A}$ can be viewed as Maurer-Cartan elements of a suitable differential graded Lie algebra $L$. In particular we show that $\mathcal{MC}(L)$, the Deligne groupoid of $L$, is in 1-1 correspondence with the non-abelian cohomology $H^2_{nab}(\mathcal{B},\mathcal{A})$.
Central extensions of Steinberg Lie superalgebras of small rank
A.V.Mikhalev和I.A.Pinchuk在[MP]中证明了Steinberg李超代数$\st$的第二同调群$H_2(\st)$对于$m+n\geq 5$是平凡的。在本文中，我们将工作$H_2(\st)$明确为$m+n=3, 4$。
A Cohomological Characterization of Leibniz Central Extensions of Lie Algebras
主要受Pirashvili关于Leibniz代数的谱序列的启发，基于推论3.3和定理3.5给出了李代数的Leibniz中心扩张的上同调刻画.特别地，作为应用，我们得到了Kac-Moody代数的\cite{Gao2}中Gao主要定理的上同调形式，并回答了\cite{LH}中的一个问题.
Extensions of Peripheric Extended Twists and Inhomogeneous Lie Algebras
介绍了Lyakhovsky和Del Olmo最近提出的外围延伸扭曲的单扩张。给出了扭曲元的显式表示，并证明了新扭曲元和周边扩张扭曲元都适用于变形非齐次李代数，如isu（n），iso（n），（1+n）维Schroedinger代数和Poincare代数.
Quasi-hom-Lie Algebras, Central Extensions and 2-cocycle-like Identities
本文首先引入拟hom-李代数的概念，它是作者在前一篇文章中引入的hom-李代数的自然推广。准Hom-李代数也包括特殊情况（颜色）李代数和超代数，并且可以被看作是这些通过同态、扭曲雅可比恒等式和斜对称的变形。这些拟自李代数的自然领域是作为Laurent多项式$\C[t,t^{-1}]$上导子的Witt代数$\Witt$的广义变形。我们还发展了qhl-代数的中心扩张理论，它可以用来变形和推广Virasoro代数的中心扩张变形的Witt型代数在这里构造。此外，我们给出了一些其他有趣的例子quasi-hom-李代数，其中变形的循环代数。
Description de la structure de certaines superalgèbres de Lie quadratiques via la notion de $T^*$-extension
本文引入李超代数${\mathfrak g}$的$T^*-$扩张$T^*{\mathfrak g}$的概念，即${\mathfrak g}$通过其对偶空间${\mathfrak g}^*$的扩张.自然配对在$T^*{\mathfrak g}$上诱导出一个偶超对称非退化双线性形式$B$，它是不变的（$B([X,Y],Z)=B(X,[Y,Z])$ for all $X,Y,Z \in T^*{\mathfrak g}$），即二次（或度量化或正交）李超代数的结构。这些扩张可以用${\mathfrak g}$的第三偶标量上同调群来分类。此外，我们表明，所有有限维二次李超代数${\mathfrak a}={\mathfrak a}_{\bar{0}} \oplus {\mathfrak a}_{\bar{1}}$是幂零的，或可解的，使$[{\mathfrak a}_{\bar{1}},{\mathfrak a}_{\bar{1}}]\subset [{\mathfrak a}_{\bar{0}},{\mathfrak a}_{\bar{0}}]$可以通过$T^*-$的情况下，特征零代数闭域的扩张。
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…
Central Extensions of the Quasi-orthogonal Lie algebras
本文用分次压缩的方法从so（N+1），N任意确定了一族李代数的中心扩张.所有的非齐次正交代数和伪正交代数都是这个家族的成员，以及大量的其他非半单代数，它们都至少有一个半直结构（在某些情况下有两个或更多）。给出了它们的二阶上同调群H^2（G，R）的维数及其中心扩张的显式表达式.
扫码添加微信好友，提出您的宝贵建议 👇
💡 备注请填写：网站反馈
发表机构由 AI 从论文文本抽取，如发现错误，欢迎反馈修正建议。