论文标题
Rota-baxter操作员在共同霍普夫代数上
Rota-Baxter operators on cocommutative Hopf algebras
论文作者
论文摘要
我们将Rota-baxter操作员的概念概括为基团的组，而重量1的Rota-baxter操作员在Lie代数上的概念，并定义并研究了Rota-Baxter操作员在同时型Hopf代数$ H $上的概念。 If $H=F[G]$ is the group algebra of a group $G$ or $H=U(\mathfrak{g})$ the universal enveloping algebra of a Lie algebra $\mathfrak{g}$, then we prove that Rota-Baxter operators on $H$ are in one to one correspondence with corresponding Rota-Baxter operators on groups or Lie algebras.
We generalize the notion of a Rota-Baxter operator on groups and the notion of a Rota-Baxter operator of weight 1 on Lie algebras and define and study the notion of a Rota-Baxter operator on a cocommutative Hopf algebra $H$. If $H=F[G]$ is the group algebra of a group $G$ or $H=U(\mathfrak{g})$ the universal enveloping algebra of a Lie algebra $\mathfrak{g}$, then we prove that Rota-Baxter operators on $H$ are in one to one correspondence with corresponding Rota-Baxter operators on groups or Lie algebras.
