标题： Pre-Lie 2-bialgebras 和 2-阶经典 Yang-Baxter 方程 显示英文标题

标题： Pre-Lie 2-bialgebras and 2-grade classical Yang-Baxter equations

摘要： 我们引入了一个para-Kähler严格李2-代数的概念，这可以看作是para-Kähler李代数的范畴化。 为了通过严格预李2-代数来研究para-Kähler严格李2-代数，我们引入了严格预李2-代数的Manin三元组、匹配对和双代数理论，并建立了它们之间的等价关系。 通过李2-代数的上同调理论，我们研究了coboundary严格预李2-代数，并在严格预李2-代数中引入了2-分次经典Yang-Baxter方程。 2-分次经典Yang-Baxter方程的解有助于构造严格预李2-代数和para-Kähler严格李2-代数。 特别是，可以从严格预李2-代数自然地构造严格预李2-双代数。 显示英文摘要

摘要： We introduce a notion of a para-K\"{a}hler strict Lie 2-algebra, which can be viewed as a categorification of a para-K\"{a}hler Lie algebra. In order to study para-K\"{a}hler strict Lie 2-algebra in terms of strict pre-Lie 2-algebras, we introduce the Manin triples, matched pairs and bialgebra theory for strict pre-Lie 2-algebras and the equivalent relationships between them are also established. By means of the cohomology theory of Lie 2-algebras, we study the coboundary strict pre-Lie 2-algebras and introduce 2-graded classical Yang-Baxter equations in strict pre-Lie 2-algebras. The solutions of the 2-graded classical Yang-Baxter equations are useful to construct strict pre-Lie 2-algebras and para-K\"{a}hler strict Lie 2-algebras. In particular, there is a natural construction of strict pre-Lie 2-bialgebras from the strict pre-Lie 2-algebras.