论文标题
在3-lie代数上的共同代数的同型代数和控制代数
Cohomology and the controlling algebra of crossed homomorphisms on 3-Lie algebras
论文作者
论文摘要
在本文中，首先，我们就对另一个3-lie代数的作用进行了3个lie代数的交叉同态概念，并使用从谎言代数到半领产品的同质性代数来表征它。我们还建立了交叉同态和3个lie代数的重量1的相对旋转式运算符之间的关系。接下来，我们使用第二个共同体学组构建了三个lie代数的跨代数杂法，并对交叉同构的无限变形进行分类。最后，使用较高的衍生括号，我们构建了一个$ l_ \ infty $ - 代数，其毛rer-cartan元素是跨性同构的。因此，我们获得了扭曲的$ l_ \ infty $ -Algebra，该代数控制了给定的三个代数上给定的同构的变形。
In this paper, first we give the notion of a crossed homomorphism on a 3-Lie algebra with respect to an action on another 3-Lie algebra, and characterize it using a homomorphism from a Lie algebra to the semidirect product Lie algebra. We also establish the relationship between crossed homomorphisms and relative Rota-Baxter operators of weight 1 on 3-Lie algebras. Next we construct a cohomology theory for a crossed homomorphism on 3-Lie algebras and classify infinitesimal deformations of crossed homomorphisms using the second cohomology group. Finally, using the higher derived brackets, we construct an $L_\infty$-algebra whose Maurer-Cartan elements are crossed homomorphisms. Consequently, we obtain the twisted $L_\infty$-algebra that controls deformations of a given crossed homomorphism on 3-Lie algebras.
