论文标题
非交换性泊松双子
Noncommutative Poisson bialgebras
论文作者
论文摘要
在本文中，我们介绍了非共同泊松bialgebra的概念，并建立了匹配的对，Manin Triples和非交通性泊松型bialgebras之间的等效性。使用准代表和非交通泊松代数的相应的共同体学理论，我们研究了串联的非交通泊松双gebras，从而导致了Poisson Yang-baxter方程的引入。 Poisson Yang-Baxter方程的偏度对称解自然产生了（串联的）非共同泊松bialgebra。介绍了旋转式运算符，更普遍的o-operators在非交通性泊松代数方面以及非共同的前poisson代数，我们引入了一些特殊的非公用poisson代数在这些结构中获得的poisson yang-baxter方程的偏压对称溶液。
In this paper, we introduce the notion of a noncommutative Poisson bialgebra, and establish the equivalence between matched pairs, Manin triples and noncommutative Poisson bialgebras. Using quasi-representations and the corresponding cohomology theory of noncommutative Poisson algebras, we study coboundary noncommutative Poisson bialgebras which leads to the introduction of the Poisson Yang-Baxter equation. A skew-symmetric solution of the Poisson Yang-Baxter equation naturally gives a (coboundary) noncommutative Poisson bialgebra. Rota-Baxter operators, more generally O-operators on noncommutative Poisson algebras, and noncommutative pre-Poisson algebras are introduced, by which we construct skew-symmetric solutions of the Poisson Yang-Baxter equation in some special noncommutative Poisson algebras obtained from these structures.
