Clifford Deformations of Koszul Frobenius Algebras and Noncommutative Quadrics.

A Clifford deformation of a Koszul Frobenius algebra E is a finite dimensional Z 2 -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 D b (gr Z 2 E (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 Z 2 -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. [ABSTRACT FROM AUTHOR]