论文标题
扭曲的rota-baxter家族和NS家庭代数
Twisted Rota-Baxter families and NS-family algebras
论文作者
论文摘要
由半群索引的家族代数结构首先出现在量子场理论的重量化的代数方面。最近发现了Rota-baxter家族及其与（Tri）树突状家族代数的关系。在本文中，我们首先将$ \ Mathcal {O} $ - 运营商系列的概念视为Rota-Baxter家族的概括，并定义了产生$ \ Mathcal {O} $的关联Yang-Baxter家族的两个变体 - 运营商家庭。给定一个基础代数上的Hochschild $ 2 $ cocycle，我们还定义了一个扭曲的$ \ Mathcal {O} $ - 操作员家族（尤其是Rota-Baxter家族）的概念。我们还介绍和研究NS家庭代数是扭曲的$ \ Mathcal {O} $ - 运营商家庭的基础结构。最后，我们定义了扭曲的$ \ Mathcal {o} $ - 运营商家庭和NS家庭代数（尤其是Rota-Baxter家族和Dendriorper家族代数的共同体）的合适的共同体学，这些代数为主管的变形。
Family algebraic structures indexed by a semigroup first appeared in the algebraic aspects of renormalizations in quantum field theory. The concept of the Rota-Baxter family and its relation with (tri)dendriform family algebras have been recently discovered. In this paper, we first consider a notion of $\mathcal{O}$-operator family as a generalization of the Rota-Baxter family and define two variations of associative Yang-Baxter family that produce $\mathcal{O}$-operator families. Given a Hochschild $2$-cocycle on the underlying algebra, we also define a notion of twisted $\mathcal{O}$-operator family (in particular twisted Rota-Baxter family). We also introduce and study NS-family algebras as the underlying structure of twisted $\mathcal{O}$-operator families. Finally, we define suitable cohomology of twisted $\mathcal{O}$-operator families and NS-family algebras (in particular cohomology of Rota-Baxter families and dendriform family algebras) that govern their deformations.
