Twisted Segre products

2021/11/08 by He, Ji-Wei, Ueyama, Kenta
#FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2111.04245

Abstract

We introduce the notion of the twisted Segre product A∘_ψB of \mathbb Z-graded algebras A and B with respect to a twisting map ψ. It is proved that if A and B are noetherian Koszul Artin-Schelter regular algebras and ψ is a twisting map such that the twisted Segre product A∘_ψB is noetherian, then A∘_ψB is a noncommutative graded isolated singularity. To prove this result, the notion of densely (bi-)graded algebras is introduced. Moreover, we show that the twisted Segre product A∘_ψB of A=k[u,v] and B=k[x,y] with respect to a diagonal twisting map ψ is a noncommutative quadric surface (so in particular it is noetherian), and we compute the stable category of graded maximal Cohen-Macaulay modules over it.

Related

• Skew Knörrer's periodicity Theorem
• Stable Categories of Graded Maximal Cohen-Macaulay Modules over Noncommutative Quotient Singularities
• Noncommutative resolutions of AS-Gorenstein isolated singularites
• Generalized Knörrer's Periodicity Theorem
• Clifford deformations of Koszul Frobenius algebras and noncommutative quadrics