Given any integers a,b,c, and d with a 〉 1, c ≥ 0, b ≥ a＋c, and d ≥ b ＋ c, the notion of （a, b, c, d）-Koszul algebra is introduced, which is another class of standard graded algebras with ＂nonpure＂ resolutio...Given any integers a,b,c, and d with a 〉 1, c ≥ 0, b ≥ a＋c, and d ≥ b ＋ c, the notion of （a, b, c, d）-Koszul algebra is introduced, which is another class of standard graded algebras with ＂nonpure＂ resolutions, and includes many Artin-Schelter regular algebras of low global dimension as specific examples. Some basic properties of （a, b, c, d）-Koszul algebras/modules are given, and several criteria for a standard graded algebra to be （a, b, c, d）- Koszul are provided.展开更多
基金This work was supported by the National Natural Science Foundation of China （Grant Nos. 11571316, 11001245） and the Natural Science Foundation of Zhejiang Province （Grant No. LY16A010003）.
文摘Given any integers a,b,c, and d with a 〉 1, c ≥ 0, b ≥ a＋c, and d ≥ b ＋ c, the notion of （a, b, c, d）-Koszul algebra is introduced, which is another class of standard graded algebras with ＂nonpure＂ resolutions, and includes many Artin-Schelter regular algebras of low global dimension as specific examples. Some basic properties of （a, b, c, d）-Koszul algebras/modules are given, and several criteria for a standard graded algebra to be （a, b, c, d）- Koszul are provided.
