Semisimplicity of adjacency algebras of coherent configurations

It is known that the Frame number characterizes the semisimplicity of adjacency algebras of association schemes (see [A. Hanaki, “Semisimplicity of adjacency algebras of association schemes”, J. Algebra, 225 (2000), 124–129]). Coherent configurations are a generalization of association schemes. In this paper, we aim to extend this fact to coherent configurations.