The Terwilliger algebra of an association scheme of order n introduced in  is a subalgebra of the matrix algebra of all n×n matrices. Terwilliger algebras of wreath products of special association schemes are studied in several papers. In this paper we study the Terwilliger algebra of the wreath product T|S of two arbitrary association schemes S and T. We will express the Terwilliger algebra of T|S and its primitive central idempotents in terms of the Terwilliger algebras of S and T and their primitive central idempotents. The known results of Hanaki, Kim, etc. (cf. [7,10]) are special cases of our results.
- Association schemes
- Bose-Mesner algebras
- Coherent configurations
- Primitive central idempotents
- Terwilliger algebras