Rank two Artin-Schelter regular algebras and non commuting derivations

Vincent Beck, César Lecoutre

If $\Delta$ and $\Gamma$ are two derivations of a commutative algebra $A$ such that $\Delta \Gamma -\Gamma \Delta =\Delta$ is locally nilpotent, one can endow $A$ with a new product $\ast$ whose filtered semiclassical l…