Structures of W(2.2) Lie conformal algebra
Structures of W(2.2) Lie conformal algebra
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DOI：
10.1515/math-2016-0054
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发表时间：
2016-01
期刊：
影响因子：
1.7
通讯作者：
Lamei Yuan;Henan Wu
中科院分区：
文献类型：
--
作者：
Lamei Yuan;Henan Wu
本文研究了W（2，2）李共形代数，它具有一个自由的n [n]-基{L，M}使得[LλL]=（n +2 λ）L，[LλM]=（n +2 λ）M，[MλM]=0 $\开始{方程}[{L_\lambda }L] =（\partial + 2\lambda）L，[{L_\lambda }M] =（\partial + 2\lambda）M，[{M_\lambda }M] = 0]\end{equation}$ .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具有系数的上同调。特别是，我们确定其上同调与平凡系数的基本和减少复杂。
Abstract The purpose of this paper is to study W(2, 2) Lie conformal algebra, which has a free ℂ[∂]-basis {L, M} such that [LλL]=(∂+2λ)L,[LλM]=(∂+2λ)M,[MλM]=0 $\begin{equation}[{L_\lambda }L] = (\partial + 2\lambda )L,[{L_\lambda }M] = (\partial + 2\lambda )M,[{M_\lambda }M] = 0]\end{equation}$ . In this paper, we study conformal derivations, central extensions and conformal modules for this Lie conformal algebra. Also, we compute the cohomology of this Lie conformal algebra with coefficients in its modules. In particular, we determine its cohomology with trivial coefficients both for the basic and reduced complexes.