论文标题
相对rota-baxter leibniz代数，它们的表征和共同学
Relative Rota-Baxter Leibniz algebras, their characterization and cohomology
论文作者
论文摘要
最近，从共同的角度研究了在文献中广泛研究了相对rota-baxter（Lie/cossociative）代数。在本文中，我们将相对Rota-Baxter Leibniz代数（RRB Leibniz代数）视为我们研究的对象。我们构建了一个$ l_ \ infty $ -Algebra，其特征是RRB Leibniz代数为其Maurer-Cartan元素。然后，我们定义了RRB Leibniz代数的表示形式，并在表示中以系数引入同胞。作为共同体的应用，我们研究了RRB Leibniz代数的变形和Abelian扩展。
Recently, relative Rota-Baxter (Lie/associative) algebras are extensively studied in the literature from cohomological points of view. In this paper, we consider relative Rota-Baxter Leibniz algebras (rRB Leibniz algebras) as the object of our study. We construct an $L_\infty$-algebra that characterizes rRB Leibniz algebras as its Maurer-Cartan elements. Then we define representations of an rRB Leibniz algebra and introduce cohomology with coefficients in a representation. As applications of cohomology, we study deformations and abelian extensions of rRB Leibniz algebras.
