论文标题
免费$ω$ -Rota-baxter Systems和Gröbner-Shirshov基地
Free $Ω$-Rota-Baxter systems and Gröbner-Shirshov bases
论文作者
论文摘要
在本文中，我们提出了$ω$ -Rota-baxter系统的概念，该系统是Rota-Baxter系统的概括，重量为零的$ω$ -ROTA-BAXTER代数。在操作代数的框架中，我们获得了一个免费的$ω$ -Rota-baxter系统的线性基础，用于扩展的diassociative semigroup $ω$，就括号内的单词和Gröbner-Shirshov Base的方法而言。作为应用程序，我们介绍了Rota-baxter系统家族代数的概念和匹配的rota-baxter系统，作为$ω$ -Rota-baxter系统的特殊情况，并构建其自由对象。同时，通过新方法重建了免费的$ω$ -Rota-baxter代数，重量为零，免费的rota-baxter系统，免费的rota-baxter家族代数和免费匹配的rota-baxter代数。
In this paper, we propose the concept of an $Ω$-Rota-Baxter system, which is a generalization of a Rota-Baxter system and an $Ω$-Rota-Baxter algebra of weight zero. In the framework of operated algebras, we obtain a linear basis of a free $Ω$-Rota-Baxter system for an extended diassociative semigroup $Ω$, in terms of bracketed words and the method of Gröbner-Shirshov bases. As applications, we introduce the concepts of Rota-Baxter system family algebras and matching Rota-Baxter systems as special cases of $Ω$-Rota-Baxter systems, and construct their free objects. Meanwhile, free $Ω$-Rota-Baxter algebras of weight zero, free Rota-Baxter systems, free Rota-Baxter family algebras and free matching Rota-Baxter algebras are reconstructed via new method.
