Abstract
We study the algebra Rp,q generated by the Eulerian derivatives for two parameters p and q. Subject to certain conditions on the parameters, we show that Rp,q is a finitely presented N-graded algebra of Gelfand–Kirillov dimension 3. We establish a criterion for the cyclic module Rp,q/Rp,qf to be Noetherian, where f is homogeneous of degree 1. For some choices of the parameters, this criterion always holds and we know of no situation where it fails. It is not known whether Rp,q is Noetherian. We classify the point modules for Rp,q and determine the normal elements and graded automorphisms for Rp,q.
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