To enrich the singularity representation theory and classification results of non-commutative quadratic hy-persurface singularity,this paper takes graded skew polynomial algebras as the research object,discusses the quadratic reg-ular central elements and characterizes the stable categories of the corresponding maximal Cohen-Macaulay module cate-gories.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 hypersur-face algebras are calculated.The result is helpful for the classification of non-commutative quadric hypersurface algebras.
维普
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