Some quantum P3s with infinitely many points

Abstract

We consider graded Clifford algebras on n generators in the spirit of Artin, Tate and Van den Bergh’s non-commutative algebraic geometry. We give an algorithm for counting the point modules over such an algebra, and prove that a generic graded Clifford algebra on four generators has defining relations which are determined by their zero locus in P3 × P3 Furthermore, we find a 1-parameter family of iterated Ore extensions on four generators which are deformations of a graded Clifford algebra such that the generic member has precisely one point module and a 1-dimensional family of line modules.