On Knörrer periodicity for quadric hypersurfaces in skew projective spaces

2018/09/12 by Kenta Ueyama, Ueyama, Kenta
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Advanced Topics in Algebra #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1809.04305

Abstract

We study the structure of the stable category \mathsf\underlineCM^{\mathbb Z}(S/(f)) of graded maximal Cohen-Macaulay module over S/(f) where S is a graded (± 1)-skew polynomial algebra in n variables of degree 1, and f =x₁² + ⋯ +x_n². If S is commutative, then the structure of \mathsf\underlineCM^{\mathbb Z}(S/(f)) is well-known by Knörrer's periodicity theorem. In this paper, we prove that if n≤ 5, then the structure of \mathsf\underlineCM^{\mathbb Z}(S/(f)) is determined by the number of irreducible components of the point scheme of S which are isomorphic to \mathbb P¹.

Citations

• Equivalences for noncommutative projective spaces

Related

• Combinatorial study of stable categories of graded Cohen--Macaulay modules over skew quadric hypersurfaces
• Skew Knörrer's periodicity Theorem
• Generalized Knörrer's Periodicity Theorem
• Some extensions of theorems of Knörrer and Herzog-Popescu
• Clifford deformations of Koszul Frobenius algebras and noncommutative quadrics