论文标题
谎言三重系统上的O-操作员
O-operators on Lie triple systems
论文作者
论文摘要
本文的目的是研究$ \ Mathcal {o} $ - 运算符的谎言三重系统的共同体和变形。我们将$ \ MATHCAL {O} $ - 运营商$ t $的共同体定义为由$ t $ th $ t $带有系数的特定谎言三重系统的Lie-Yamaguti共同体。然后，我们考虑$ \ Mathcal {O} $的无限和形式变形 - 从共同体观点来看。此外，我们提供了$ \ Mathcal {O} $ - 运算符和相关的Lie Triple Systems之间的关系。
The purpose of this paper is to study cohomology and deformations of $\mathcal{O}$-operators on Lie triple systems. We define a cohomology of an $\mathcal{O}$-operator $T$ as the Lie-Yamaguti cohomology of a certain Lie triple system induced by $T$ with coefficients in a suitable representation. Then we consider infinitesimal and formal deformations of $\mathcal{O}$-operators from cohomological viewpoint. Moreover we provide relationships between $\mathcal{O}$-operators on Lie algebras and associated Lie triple systems.
