Modules of codimension one over Weyl algebras (Q1908463)

This paper studies the structure of the category of all modules over a Weyl algebra with a characteristic variety which is a generic hypersurface, and therefore all its objects have Gelfand-Kirillov codimension one. An introduction and some basic results are proved in the first two sections. In section 3 it is proven that this category has infinitely many non-isomorphic irreducible modules of every possible multiplicity. In section 4 the first extension groups for some irreducible modules are calculated, and the author shows that \(\text{Ext}^1(M,N)\) may be infinite dimensional in contrast with the holonomic case. In the least section, the previous results are used to construct families of non-cyclic projective ideals for the Weyl algebra.