Noncommutative Knörrer periodicity via equivariantization

2025/09/06 by Xiao‐Wu Chen, Chen, Xiao-Wu, Wenchao Wu +1
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Mechanics and Non-Hermitian Physics #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2509.05725

openalex publication_date 2025/09/06 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28

Abstract

We establish noncommutative Knörrer periodicity for projective-module factorizations over an arbitrary ring, using the equivariantization theory with respect to various actions by a cyclic group of order two. We obtain an explicit quasi-inverse of the periodicity. We compare the periodicity with a certain tensor functor between big singularity categories.

Citations

• Module factorizations
• Matrix factorizations, Reality and Knörrer periodicity
• Purity, ascent, and periodicity for Gorenstein flat cotorsion modules
• Noncommutative Kn "orrer periodicity and noncommutative Kleinian\n singularities
• Noncommutative matrix factorizations with an application to skew exterior algebras
• Homological mirror symmetry for singularities
• Monadicity theorem and weighted projective lines of tubular type
• On equivariant triangulated categories
• Periodic free resolutions from twisted matrix factorizations
• On braided fusion categories I
• On braided fusion categories I
• Phases Of N=2 Theories In 1+1 Dimensions With Boundary

Related

• Matrix factorizations, Reality and Knörrer periodicity
• Périodicité de Knörrer étendue
• Generalized Knörrer's Periodicity Theorem
• Noncommutative Kn "orrer periodicity and noncommutative Kleinian\n singularities
• Knoerrer Periodicity and Bott Periodicity