Clifford Deformations of Koszul Frobenius Algebras and Noncommutative Quadrics

A Clifford deformation of a Koszul Frobenius algebra Formula: see text is a finite dimensional Formula: see text-graded algebra Formula: see text, which corresponds to a noncommutative quadric hypersurface Formula: see text for some central regular element Formula: see text. It turns out that the bounded derived category Formula: see text is equivalent to the stable category of the maximal Cohen-Macaulay modules over Formula: see text provided that Formula: see text is noetherian. As a consequence, Formula: see text is a noncommutative isolated singularity if and only if the corresponding Clifford deformation Formula: see text is a semisimple Formula: see text-graded algebra. The preceding equivalence of triangulated categories also indicates that Clifford deformations of trivial extensions of a Koszul Frobenius algebra are related to Knörrer's periodicity theorem for quadric hypersurfaces. As an application, we recover Knörrer's periodicity theorem without using matrix factorizations.