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三维半群代数
引用本文:纪影丹,罗彦锋.三维半群代数[J].数学年刊A辑(中文版),2019,40(4):377-398.
作者姓名:纪影丹  罗彦锋
作者单位:广东工业大学应用数学学院, 广州 510520.,兰州大学数学与统计学院, 兰州 730000.
摘    要:首先给出代数闭域上三维半群代数的幂等元集和Jacobson根, 并且刻画了三维半群代数的同构类. 通过计算箭图, 研究了三维代数的表示型. 进一步, 证明一个三维(或者二维) 半群代数是胞腔的, 当且仅当它是交换的. 作为推论, 得到一个左零带所对应的半群代数是胞腔的, 当且仅当这个左零带是一个半格.

关 键 词:Semigroup  algebras    Isomorphism  classes    Quivers    Cellular  algebras

Three Dimensional Semigroup Algebras
JI Yingdan and LUO Yanfeng.Three Dimensional Semigroup Algebras[J].Chinese Annals of Mathematics,2019,40(4):377-398.
Authors:JI Yingdan and LUO Yanfeng
Institution:School of Applied Mathematics, Guangdong University of Technology, Guangzhou 510520, China. and School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China.
Abstract:In this paper, the authors provide the idempotent sets and Jacobson radicals of all three dimensional semigroup algebras, and then classify these algebras up to isomorphism, where the results depend on the characteristic of the ground algebraically closed field. Then the representation type of these semigroup algebras are investigated by computing certain quivers. The authors also prove that a three (resp., two) dimensional semigroup algebra is cellular if and only if it is commutative. As a by-product, it is showed that the semigroup algebra of a left zero band is cellular if and only if it is a semilattice.
Keywords:Semigroup algebras    Isomorphism classes    Quivers    Cellular algebras
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