Journal
GRAPHS AND COMBINATORICS
Volume 37, Issue 5, Pages 1521-1529Publisher
SPRINGER JAPAN KK
DOI: 10.1007/s00373-021-02363-0
Keywords
Association scheme; Terwilliger algebra
Categories
Funding
- JSPS KAKENHI [JP17K05165]
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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.
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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