Clifford Deformations of Koszul Frobenius Algebras and Noncommutative Quadrics  

作　　者：Jiwei He Yu Ye 

机构地区：[1]Department of Mathematics,Hangzhou Normal University,Hangzhou 311121,China [2]School of Mathematical Sciences,University of Science and Technology of China Hefei 230026,China

出　　处：《Algebra Colloquium》2024年第1期63-82,共20页代数集刊（英文版）

基　　金：supported by ZJNSF(LY19A010011);NSFC(11971141,12371017);supported by NSFC(11971449,12131015,12371042).

摘　　要：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.

关 键 词：Koszul Frobenius algebra Clifford deformation noncommutative quadric hypersurface maximal Cohen-Macaulay module 

分 类 号：O15[理学—数学]