Terwilliger algebras of wreath products by 3-equivalent schemes

TL;DR

This paper investigates the structure of Terwilliger algebras associated with wreath products involving 3-equivalent schemes, extending previous work on one-class and quasi-thin schemes.

Contribution

It provides a detailed analysis of Terwilliger algebras for wreath products by 3-equivalent schemes, a new class not previously studied.

Findings

Characterization of Terwilliger algebras for 3-equivalent schemes

Extension of known results to a broader class of schemes

New structural insights into wreath product algebras

Abstract

Recently G. Bhattacharyya, S.Y. Song and R. Tanaka began to study Terwilliger algebras of wreath products of one-class association schemes. K. Kim determined the structure of Terwilliger algebras of wreath products by one-class association schemes or quasi-thin schemes. In this paper, we study Terwilliger algebras of wreath products by $3$-equivalenced schemes.