Title: On Terwilliger $\mathbb{F}$-algebras of direct products of group divisible association schemes Show Chinese title

Title: 关于群可分关联方案直积的Terwilliger$\mathbb{F}$-代数

Abstract: The Terwilliger algebras of association schemes over an arbitrary field $\mathbb{F}$ were briefly called the Terwilliger $\mathbb{F}$-algebras of association schemes in [9]. In this paper, the Terwilliger $\mathbb{F}$-algebras of direct products of group divisible association schemes are studied. The centers, the semisimplicity, the Jacobson radicals and their nilpotent indices, the Wedderburn-Artin decompositions of the Terwilliger $\mathbb{F}$-algebras of direct products of group divisible association schemes are obtained. Show Chinese abstract

Abstract: 关于任意域上的关联系的Terwilliger代数 $\mathbb{F}$在[9]中被简称为关联系的Terwilliger$\mathbb{F}$-代数。 本文研究了群可分关联系直积的Terwilliger$\mathbb{F}$-代数。 得到了群可分关联系直积的Terwilliger$\mathbb{F}$-代数的中心、半单性、Jacobson根及其幂零指数、以及Wedderburn-Artin分解。