On Terwilliger 𝔽-algebras of factorial association schemes II

The Terwilliger algebras of association schemes over an arbitrary field [Formula: see text] were called the Terwilliger [Formula: see text]-algebras of association schemes in [10]. In [7], He and Jiang studied the Terwilliger [Formula: see text]-algebras of factorial association schemes. In this paper, we continue studying the Terwilliger [Formula: see text]-algebras of factorial association schemes. We get all block idempotents of the Terwilliger [Formula: see text]-algebras of factorial association schemes. We get the [Formula: see text]-dimensions, the centers, the Jacobson radicals of the block algebras of the Terwilliger [Formula: see text]-algebras of factorial association schemes.