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Let $E$ be a Koszul Frobenius algebra. A Clifford deformation of $E$ is afinite dimensional $\mathbb Z_2$-graded algebra $E(\theta)$, which correspondsto a noncommutative quadric hypersurface $E^!/(z)$, for some central regularelement $z\in E^!_2$. It turns out that the bounded derived category$D^b(\text{gr}_{\mathbb Z_2}E(\theta))$ is equivalent to the stable category ofthe maximal Cohen-Macaulay modules over $E^!/(z)$ provided that $E^!$ isnoetherian. As a consequence, $E^!/(z)$ is a noncommutative isolatedsingularity if and only if the corresponding Clifford deformation $E(\theta)$is a semisimple $\mathbb Z_2$-graded algebra. The preceding equivalence oftriangulated categories also indicates that Clifford deformations of trivialextensions of a Koszul Frobenius algebra are related to the Kn\"{o}rrerPeriodicity Theorem for quadric hypersurfaces. As an application, we recoverKn\"{o}rrer Periodicity Theorem without using of matrix factorizations.

Clifford deformations of Koszul Frobenius algebras and noncommutative quadrics