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Modular Terwilliger Algebras of Association Schemes

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Abstract

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.

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Acknowledgements

This work was supported by JSPS KAKENHI Grant Number JP17K05165.

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Correspondence to Akihide Hanaki.

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Dedicated to Professor Eiichi Bannai and Professor Hikoe Enomoto on their 75th birthday.

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Hanaki, A. Modular Terwilliger Algebras of Association Schemes. Graphs and Combinatorics 37, 1521–1529 (2021). https://doi.org/10.1007/s00373-021-02363-0

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  • DOI: https://doi.org/10.1007/s00373-021-02363-0

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