李三元系统上o算子的上同调与变形

IF 0.5 4区数学 Q3 MATHEMATICS

Journal of Mathematical Physics Analysis Geometry Pub Date : 2023-08-01 DOI:10.1063/5.0118911

T. Chtioui, A. Hajjaji, S. Mabrouk, Abdenacer Makhlouf

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引用次数: 4

摘要

本文首先给出了一个分阶李代数，它的毛雷尔-卡坦元刻画了李三系结构。在此基础上，构造了一个毛雷尔-卡坦元为o算子的李三元代数，研究了李三元系统上o算子的上同调和变形。进一步，我们将o算子T的上同调定义为由T诱导的具有适当表示的系数的某Lie三重系统的Lie - yamaguti上同调。因此，我们从上同调的观点来考虑o算子的无穷小变形和形式变形。此外，我们还给出了李代数上的o算子与相关李三元系统之间的关系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Cohomologies and deformations of O-operators on Lie triple systems

In this paper, first, we provide a graded Lie algebra whose Maurer–Cartan elements characterize Lie triple system structures. Then, we use it to study cohomology and deformations of O-operators on Lie triple systems by constructing a Lie 3-algebra whose Maurer–Cartan elements are O-operators. Furthermore, we define a cohomology of an O-operator T as the Lie–Yamaguti cohomology of a certain Lie triple system induced by T with coefficients in a suitable representation. Therefore, we consider infinitesimal and formal deformations of O-operators from a cohomological viewpoint. Moreover, we provide relationships between O-operators on Lie algebras and associated Lie triple systems.

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来源期刊

Journal of Mathematical Physics Analysis Geometry PHYSICS, MATHEMATICAL-

CiteScore

0.70

自引率

20.00%

发文量

审稿时长

>12 weeks

期刊介绍： Journal of Mathematical Physics, Analysis, Geometry (JMPAG) publishes original papers and reviews on the main subjects: mathematical problems of modern physics; complex analysis and its applications; asymptotic problems of differential equations; spectral theory including inverse problems and their applications; geometry in large and differential geometry; functional analysis, theory of representations, and operator algebras including ergodic theory. The Journal aims at a broad readership of actively involved in scientific research and/or teaching at all levels scientists.