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On Terwilliger $\mathbb{F}$-algebras of direct products of group divisible association schemes
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abstract
The Terwilliger algebras of association schemes over an arbitrary field $\mathbb{F}$ were briefly called the Terwilliger $\mathbb{F}$-algebras of association schemes in [9]. In this paper, the Terwilliger $\mathbb{F}$-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 $\mathbb{F}$-algebras of direct products of group divisible association schemes are obtained.
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