Terwilliger algebras of wreath products by quasi-thin schemes

TL;DR

This paper investigates the structure of Terwilliger algebras for wreath products involving quasi-thin schemes, extending previous results that focused on thin or one-class schemes, thereby broadening the understanding of algebraic structures in association schemes.

Contribution

It generalizes prior work by analyzing Terwilliger algebras of wreath products with quasi-thin schemes, expanding the class of schemes studied.

Findings

Provides a structural description of Terwilliger algebras for wreath products with quasi-thin schemes

Extends known results from thin schemes to quasi-thin schemes

Enhances understanding of algebraic properties in association schemes

Abstract

The structure of Terwilliger algebras of wreath products by thin schemes or one-class schemes was studied in [A. Hanaki, K. Kim, Y. Maekawa, Terwilliger algebras of direct and wreath products of association schemes, J. Algebra 343 (2011) 195--200]. In this paper, we will consider the structure of Terwilliger algebras of wreath products by quasi-thin schemes. This gives a generalization of their result.