Graded Lie Algebras of Dimension Five and Some Artin-Schelter Regular Algebras

作     者：Yuan Shen 

作者机构：Department of Mathematics Zhejiang Sci-Tech University Hangzhou 310018 China 

出 版 物：《Algebra Colloquium》 (代数集刊（英文版）)

年 卷 期：2019年第26卷第2期

页      面：243-258页

核心收录：

学科分类：07[理学] 0701[理学-数学] 

基　　金：NSFC (No. 11701515) ZJNSF (No. LY18A010028) Science Foundation of Zhejiang Sci-Tech University (ZSTU)(No. 16062066-Y). 

主　　题：Artin-Schelter regular algebras graded Lie algebras Nakayama automorphisms 

摘      要：In this paper, we show that there are only seven graded Lie algebras of dimension 5 generated in degree 1 up to isomorphism. By parameterizing the relations of the universal enveloping algebras of three of those graded Lie algebras, we construct some new Artin-Schelter regular algebras of global dimension 5. We prove that those algebras are all strongly noetherian, Auslander regular and Cohen-Macaulay, and describe their Nakayama automorphisms.