On graded symmetric cellular algebras
On graded symmetric cellular algebras
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论分级对称元胞代数
DOI：
10.1017/s1446788719000223
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发表时间：
2020
影响因子：
0.7
通讯作者：
Zhao Deke
中科院分区：
文献类型：
--
作者：
Li Yanbo;Zhao Deke
设$A=\bigoplus _{i\in \mathbb{Z}}A_{i}$是有限维分次对称胞腔代数，其齐次对称化迹为$d$。证明了若$d\neq 0$，则$A_{-d}$包含Higman理想$H（A）$和$\dim H（A）\leq \dim A_{0}$，并给出了$A$关于$A_{0}$的中心化子的半单性判据.
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 $A_{0}$.