几类新的6维Artin-Schelter正则代数

打开文本图片集

【Abstract]Toenrich thecontentof higher-dimensional Artin-Schelterregularalgebras，the paper focusesonthe studyof positively gradedLiealgebrasofdimension6generated indegree 1，particularlyinvestigating thecase with fivegenerators.It is discovered that there areonly two gradedLiealgebrasunder thiscondition.Byparameterizing therelationsof the universal enveloping algebras of these two graded Lie algebras，we construct some new Artin-Schelter regular algebras of global dimension6.And we prove that those algebras are allstrongly Noetherian，Auslander regular and Cohen-Macaulay， and describe their Nakayama automorphisms.

[Key words]Artin-Schelter regular algebras; positively graded Lie algebras; universal enveloping algebras; Nakayama automorphisms

[中图分类号】0153.3 [文献标识码］A [文章编号]1674-3229（2025）01-0005-08

0 引言

Artin-Schelter正则代数于上世纪80年代末提出，被认为是非交换射影空间的齐次坐标环，亦被看作交换多项式代数在非交换层面的对照，是非交换代数几何与非交换代数领域的重要研究对象。（剩余2363字）