| 纪影丹,罗彦锋.三维半群代数[J].数学年刊A辑,2019,40(4):377~398 |
| 三维半群代数 |
| Three Dimensional Semigroup Algebras |
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| DOI：10.16205/j.cnki.cama.2019.0029 |
| 中文关键词: Semigroup algebras, Isomorphism classes, Quivers, Cellular algebras |
| 英文关键词:Semigroup algebras, Isomorphism classes, Quivers, Cellular algebras |
| 基金项目: |
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| 中文摘要: |
| 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. |
| 英文摘要: |
| 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. |
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