Modular Adjacency Algebras of Hamming Schemes
نویسنده
چکیده
To each association scheme G and to each field R, there is associated naturally an associative algebra, the so-called adjacency algebra RG of G over R. It is well-known that RG is semisimple if R has characteristic 0. However, little is known if R has positive characteristic. In the present paper, we focus on this case. We describe the algebra RG if G is a Hamming scheme (and R a field of positive characteristic). In particular, we show that, in this case, RG is a factor algebra of a polynomial ring by a monomial ideal.
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