2021/07/14 by Ji-Wei He, He, Ji-Wei, Xin-Chao Ma +3
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Nonlinear Waves and Solitons #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2107.06438
openalex publication_date 2021/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let A be a noetherian Koszul Artin-Schelter regular algebra, and let f∈ A2 be a central regular element of A. The quotient algebra A/(f) is usually called a (noncommutative) quadric hypersurface. In this paper, we use the Clifford deformation to study the quadric hypersurfaces obtained from the tensor products. We introduce a notion of simple graded isolated singularity and proved that, if B/(g) is a simple graded isolated singularity of 0-type, then there is an equivalence of triangulated categories \underlinemcm A/(f)≅\underlinemcm (A⊗ B)/(f+g) of the stable categories of maximal Cohen-Macaulay modules. This result may be viewed as a generalization of Knörrer's periodicity theorem. As an application, we study the double branch cover (A/(f))^#=A[x]/(f+x2) of a noncommutative conic A/(f).