Centers of symmetric cellular algebras

Abstract

Let $R$ be an integral domain and $A$ a symmetric cellular algebra over $R$ with a cellular basis $\{C_{S,T}^\lam \mid \lam\in\Lambda, S,T\in M(\lam)\}$. We will construct an ideal $L(A)$ of the center 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 non-isomorphic simple $A$-modules.