Let $\mathbb{ F}$ be an arbitrary field. In this paper, we continue studying the Terwilliger algebras of association schemes over $\mathbb{ F}$ that were called the Terwilliger $\mathbb{ F}$-algebras of association schemes in [8]. We determine the algebraic structures of the Terwilliger $\mathbb{ F}$-algebras of the association schemes induced from the Cayley tables of elementary abelian $2$-groups, which provides infinite many examples and counterexamples for the study of the Terwilliger $\mathbb{ F}$-algebras of association schemes.
Categories: math.CO math.RT