On Terwilliger \mathbbF-algebras of factorial association schemes

2025/10/27 by He, Jiu-Yang, Jiang, Yu
#05E16 #05E30 #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2510.23593

Abstract

The Terwilliger algebras of association schemes over an arbitrary field \mathbbF were called the Terwilliger \mathbbF-algebras of association schemes in [9]. In this paper, we study the Terwilliger \mathbbF-algebras of factorial association schemes. We determine the centers, the semisimplicity, the Jacobson radicals and their nilpotent indices, the Wedderburn-Artin decompositions of the Terwilliger \mathbbF-algebras of factorial association schemes. Moreover, we determine all Terwilliger \mathbbF-algebras of factorial association schemes that are the symmetric \mathbbF-algebras or the Frobenius \mathbbF-algebras.

Citations

• Structure of Terwilliger algebras of quasi-thin association schemes
• A note on modular Terwilliger algebras of association schemes
• More on the Terwilliger algebra of Johnson schemes

Related

• On Terwilliger \mathbbF-algebras of factorial association schemes
• On Terwilliger \mathbbF-algebras of direct products of group divisible association schemes
• On Terwilliger \mathbbF-algebras of quasi-thin association schemes
• Terwilliger \mathbbF-algebras of certain Cayley tables
• On the Terwilliger algebra of the group association scheme of C_n \rtimes C₂