论文标题
前代代数
Pre-Leibniz algebras
论文作者
论文摘要
leibniz前代数的概念最近在莱布尼兹代数的Rota-baxter操作员研究中引入。在本文中，我们首先构建了一个分级的谎言代数，其毛勒 - 卡丹元素是前代代数。使用这种表征，我们定义了leibniz前代数的共同体，并具有表示为代表的系数。该协同学被证明可以分裂莱布尼兹代数的loday-pirashvili共同体。作为我们的共同体的应用，我们研究了前代数的正式和有限级阶变形。最后，我们定义同型前代代数，并分类一些特殊类型的同型前代代数代数。
The notion of pre-Leibniz algebras was recently introduced in the study of Rota-Baxter operators on Leibniz algebras. In this paper, we first construct a graded Lie algebra whose Maurer-Cartan elements are pre-Leibniz algebras. Using this characterization, we define the cohomology of a pre-Leibniz algebra with coefficients in a representation. This cohomology is shown to split the Loday-Pirashvili cohomology of Leibniz algebras. As applications of our cohomology, we study formal and finite order deformations of a pre-Leibniz algebra. Finally, we define homotopy pre-Leibniz algebras and classify some special types of homotopy pre-Leibniz algebras.
