Simple Holonomic Modules over the Second Weyl Algebra A2

Abstract

For simple generalized Weyl algebras Λ of Gelfand–Kirillov dimension 4, a class including the second Weyl algebra A2, some simple factor algebras of the universal enveloping algebra of the Lie algebra sl(2)×sl(2) and of Uqsl(2)×Uqsl(2), etc., the simple holonomic Λ-modules are classified up to pairs of irreducible elements of certain noncommutative Euclidean ring.