Notes on graded symmetric cellular algebras

Let $A={\oplus }_{i\in \mathbb{Z}}{A}_i$ be a finite dimensional graded symmetric cellular algebra with a homogeneous symmetrizing trace of degree $d$. We prove that $A_{-d}$ contains the Higman ideal $H(A)$ of the center of $A$ and $\dim H(A)\leq \dim A_{0}$if$d\neq 0$,andprovideasemisimplicitycriterionof$A$intermsofthecentralizerof$A_0$, which is a graded version of \cite[Theorem 3.2]{L}.