2019/05/12 by Ji-Wei He, Yu Ye, He, Ji-Wei +1 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1905.04699
openalex publication_date 2019/05/12 · openalex created_date 2019/05/16 · openalex updated_date 2026/07/28
Let E be a Koszul Frobenius algebra. A Clifford deformation of E is a finite dimensional \mathbb Z2-graded algebra E(θ), which corresponds to a noncommutative quadric hypersurface E^!/(z), for some central regular element z∈ E^!2. It turns out that the bounded derived category Db(gr\mathbb Z2E(θ)) is equivalent to the stable category of the maximal Cohen-Macaulay modules over E^!/(z) provided that E^! is noetherian. As a consequence, E^!/(z) is a noncommutative isolated singularity if and only if the corresponding Clifford deformation E(θ) is a semisimple \mathbb Z2-graded algebra. The preceding equivalence of triangulated categories also indicates that Clifford deformations of trivial extensions of a Koszul Frobenius algebra are related to the Knörrer Periodicity Theorem for quadric hypersurfaces. As an application, we recover Knörrer Periodicity Theorem without using of matrix factorizations.