The homogenization of the three dimensional skew polynomial algebras of type I

Abstract

This paper studies a special case of graded central extensions of three dimen-sional Artin-Schelter regular algebras, see [9, §3]. The algebras are homoge-nizations of two classes of three dimensional skew polynomial algebras. We refer to these algebras as Type I and Type II algebras. We describe the non-commutative projective geometry and compute the finite dimensional simple modules for the homogenization of Type I algebras in the case that α is not a primitive root of unity. In this case, all finite dimensional simple modules are quotients of line modules that are homogenizations of Verma modules.