On Terwilliger $${\mathbb {F}}$$-algebras of quasi-thin association schemes

In Hanaki (Graphs Combin 37:1521–1529, 2021), defined the Terwilliger algebras of association schemes over a commutative unital ring. this paper, we call field $${\mathbb {F}}$$ -algebras and study quasi-thin schemes. As main results, determine -dimensions, semisimplicity, Jacobson radicals, algebraic structures