论文标题
涉及和定向树突状代数
Involutive and oriented dendriform algebras
论文作者
论文摘要
树突状代数是确定的联想代数分裂，并且自然来自rota-baxter操作员，洗牌代数和平面二元树。在本文中，我们首先考虑参与树突形代数，它们的同谱和同型类似物。参与树突状代数的同谋分解了涉及缔合代数的Hochschild协同学。在接下来，我们引入了更一般的定向树突形代数的概念。我们为定向的树突形代数开发了一个共同体学理论，该理论与扩展密切相关，并控制树突状结构和方向的同时变形。
Dendriform algebras are certain splitting of associative algebras and arise naturally from Rota-Baxter operators, shuffle algebras and planar binary trees. In this paper, we first consider involutive dendriform algebras, their cohomology and homotopy analogs. The cohomology of an involutive dendriform algebra splits the Hochschild cohomology of an involutive associative algebra. In the next, we introduce a more general notion of oriented dendriform algebras. We develop a cohomology theory for oriented dendriform algebras that closely related to extensions and governs the simultaneous deformations of dendriform structures and the orientation.
