This research reveals properties of terwilliger algebras in group divisible association schemes, highlighting their semisimplicity and jacobson radicals.
The Terwilliger algebras of association schemes over an arbitrary field F were briefly called the Terwilliger F-algebras of association schemes in [9]. In this paper, the Terwilliger F-algebras of direct products of group divisible association schemes are studied. The centers, the semisimplicity, the Jacobson radicals and their nilpotent indices, the Wedderburn-Artin decompositions of the Terwilliger F-algebras of direct products of group divisible association schemes are obtained.
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Yu Jiang (2025) studied this question.
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