Finite-dimensional simple modules over certain iterated skew polynomial rings

Abstract

We classify the finite-dimensional simple R-modules for a class of algebras which arise as iterated skew polynomial rings in two variables over commutative K-algebras for an algebraically closed field k of arbitrary characteristic. The class includes the enveloping algebra and the quantized enveloping algebra of the Lie algebra sl(2, k), the quantized Weyl algebra in two variables, various quantum groups, and the enveloping algebra of the dispin Lie superalgebra.