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ON GRADED SYMMETRIC CELLULAR ALGEBRAS

Part of: Representation theory of rings and algebras Rings and algebras with additional structure Conditions on elements

Published online by Cambridge University Press:  29 July 2019

YANBO LI  and
DEKE ZHAO
YANBO LI*
Affiliation:
School of Mathematics and Statistics, Northeastern University at Qinhuangdao, Qinhuangdao066004, China email liyanbo707@163.com
DEKE ZHAO
Affiliation:
School of Applied Mathematics, Beijing Normal University at Zhuhai, Zhuhai519087, China email deke@amss.ac.cn
*
✉liyanbo707@163.com
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Abstract

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 $A_{0}$.

Keywords

(graded) cellular algebrasymmetric algebraHigman idealcentralizer

MSC classification

Primary: 16W50: Graded rings and modules
Secondary: 16G30: Representations of orders, lattices, algebras over commutative rings 16U70: Center, normalizer (invariant elements)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 108 , Issue 3 , June 2020 , pp. 349 - 362
Copyright
© 2019 Australian Mathematical Publishing Association Inc.

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Footnotes

Li is supported by the Natural Science Foundation of Hebei Province, China (A2017501003) and the Science and Technology support program of Northeastern University at Qinhuangdao (No. XNK201601). Zhao is supported partly by NSFC 11571341, 11671234, 11871107.

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