Completion of solvable enveloping algebras at the clique of the augmentation ideal (joint work with S.P.Smith)

Ian Musson

Abstract: We consider the completion \widehat(U) of U with respect to the filter of cofinite ideals I such that U/I is supported by the clique of the augmentation ideal. We show that \widehat(U) is the endomorphism ring of the direct sum of the injective hulls of the simple modules in the clique. Although \widehat(U) is not Noetherian it nevertheless enjoys some rather pleasant properties. For example there is a regular normalizing sequence in \widehat(U) such that if J is the ideal generated by the sequence then \widehat(U)/J is the direct product of complete commutative Noetherian regular rings. In addition \widehat(U) can be described in terms of differential operators.

created Fri Mar 17 17:17:14 PST 2000