Notes on δ-Koszul Algebras
Notes on δ-Koszul Algebras
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DOI：
10.1007/s10485-010-9224-1
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发表时间：
2012-04
影响因子：
0.6
通讯作者：
Jia-feng Lü
中科院分区：
文献类型：
--
作者：
Jia-feng Lü
本文是由Green和Marcos于2005年首次引入的δ-Koszul代数的连续工作(见Green和Marcos，Commun Algebra 33(6)：1753-1764,2005)。设为δ-Koszul模范畴。证明了当且仅当“极小马蹄引理”(简称“MHL”)成立时，保持满同态的核。在此基础上，引入了一类特殊的δ-Koszul代数-周期δ-代数，它们与Koszul代数有着密切的联系，回答了Green和Marcos提出的问题(Commun代数33(6)：1753-17642005)。最后，我们用单点扩张和扩张构造了新的周期δ-代数。
This paper is a continuous work ofδ-Koszul algebras, which were first introduced by Green and Marcos in 2005 (see Green and Marcos, Commun Algebra 33(6):1753–1764, 2005). Letbe the category ofδ-Koszul modules. It is proved thatpreserves kernels of epimorphisms if and only if the “minimal Horseshoe Lemma” (“MHL” for short) holds. Further, a special class ofδ-Koszul algebras namedperiodic δ-algebrasare introduced, which have close connection with Koszul algebras and provide answers to the questions raised by Green and Marcos (Commun Algebra 33(6):1753–1764, 2005). Finally, we construct new periodicδ-algebras from the given ones in terms ofone-point extensionandsum-extension.