CENTRES OF SYMMETRIC CELLULAR ALGEBRAS

Abstract

AbstractLet R be an integral domain and A a symmetric cellular algebra over R with a cellular basis {CλS,T∣λ∈Λ,S,T∈M(λ)}. We construct an ideal L(A) of the centre of A and prove that L(A) contains the so-called Higman ideal. When R is a field, we prove that the dimension of L(A) is not less than the number of nonisomorphic simple A-modules.