论文标题
Poisson Superbialgebras
Poisson superbialgebras
论文作者
论文摘要
我们介绍了Poisson Superbialgebra的概念，作为Drinfeld谎言Superbialgebras的类似物。我们将各种已知的结构扩展到有关谎言上的副本上的代表性，向泊松超级巨头。我们介绍了Manin Triple of Poisson Superalgebras和Poisson Superbialgebras的概念，并用匹配的Poisson Superalgebras表明它们之间的等效性。在此框架中讨论了经典的Yang-Baxter方程和关联的Yang-Baxter方程的组合。此外，我们介绍了$ \ mathcal {o} $的概念 - 权重$λ\的操作员\ Mathbb {k} $ of poisson superalgebra和poisson poisson Superalgebra的概念，并解释了它们之间的亲密关系和Poisson Superbialgebras。
We introduce the notion of Poisson superbialgebra as an analogue of Drinfeld's Lie superbialgebras. We extend various known constructions dealing with representations on Lie superbialgebras to Poisson superbialgebras. We introduce the notions of Manin triple of Poisson superalgebras and Poisson superbialgebras and show the equivalence between them in terms of matched pairs of Poisson superalgebras. A combination of the classical Yang-Baxter equation and the associative Yang-Baxter equation is discussed in this framework. Moreover, we introduce notions of $\mathcal{O}$-operator of weight $λ\in\mathbb{K}$ of a Poisson superalgebra and post-Poisson superalgebra and interpret the close relationships between them and Poisson superbialgebras.
