Let $A=\bigoplus _{i\in \mathbb{Z}}A_{i}$ be a finite-dimensional graded symmetric cellular algebra with a homogeneous symmetrizing trace of degree $d$. We prove that if $d\neq 0$ then $A_{-d}$ contains the Higman ideal $H(A)$ and $\dim H(A)\leq \dim A_{0}$, and provide a semisimplicity criterion for $A$ in terms of the centralizer of $A_{0}$.

中文翻译：

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分级对称细胞代数

让$A=\bigoplus _{i\in \mathbb{Z}}A_{i}$是具有齐次对称迹的有限维分级对称元胞代数$d$. 我们证明如果$d\neq 0$然后$A_{-d}$包含希格曼理想$H(A)$和$\dim H(A)\leq \dim A_{0}$，并为$澳元就集中器而言$A_{0}$.