Modular Terwilliger Algebras of Association Schemes

We define modular Terwilliger algebras of association schemes, Terwilliger algebras over a positive characteristic field, and consider basic properties. We give a condition for the modular Terwilliger algebra to be non-semisimple. We show that the dimension of a Terwilliger algebra of a Johnson scheme depends on the characteristic of the coefficient field. We also give some other examples.

Automated summary

This paper discusses the modular Terwilliger algebras of association schemes and those over a positive characteristic field, as well as their basic properties and conditions. It is found that the dimension of the Terwilliger algebra of a Johnson scheme depends on the characteristic of the coefficient field. Additionally, other examples are provided.