斜多项式二次超曲面代数  

Skew-Polynomials Quadric Hypersurface Algebra

作　　者：刘旸 Liu Yang(Zhejiang Sci-Tech University,Hangzhou 310018,China)

机构地区：[1]浙江理工大学,浙江杭州310018

出　　处：《廊坊师范学院学报（自然科学版）》2024年第4期5-13,共9页Journal of Langfang Normal University(Natural Science Edition)

基　　金：浙江省自然科学基金项目(LY24A010006)。

摘　　要：为丰富非交换二次超曲面代数奇点表示理论和分类结果,以分次斜多项式代数为研究对象,讨论二次正则中心元并刻画相应极大Cohen-Macaulay模范畴的稳定范畴。建立分次斜多项式系数矩阵与二次中心元之间联系,分别得到了n元(±1)-分次斜多项式和4元分次非(±1)-斜多项式的二次正则中心元的分类;通过图论方法和Clifford形变,计算了相关非交换二次超曲面代数的极大Cohen-Macaulay模范畴的稳定范畴。可为后续非交换二次超曲面代数的分类提供帮助。To enrich the singularity representation theory and classification results of non-commutative quadratic hypersurface singularity,this paper takes graded skew polynomial algebras as the research object,discusses the quadratic regular central elements and characterizes the stable categories of the corresponding maximal Cohen-Macaulay module categories.By establishing the relationship between the coefficient matrix of the graded skew polynomial and the quadratic central element,the classification of quadratic central elements of n variable graded(±1)-skew polynomial and 4 variable graded non-(±1)-skew polynomial is obtained respectively.Through the graph theory methods and Clifford deformations,the stable categories of the maximal Cohen-Macaulay module category of the related non-commutative quadric hypersurface algebras are calculated.The result is helpful for the classification of non-commutative quadric hypersurface algebras.

关 键 词：非交换二次超曲面 中心元 极大Cohen-Macaulay模范畴 Clifford形变 

分 类 号：O153.3[理学—数学]