Extensions of certain modules over the 1st weyl algebraExtensions of certain modules over the 1st weyl algebra
Faculty of Sciences. Mathematics and Computer Science
Science in China : series A : mathematics, physics, astronomy and technological sciences. - Beijing, 1989 - 1995
37(1994):5, p. 535-546
Using a method stemming from the representation theory of finite-dimensional algebra's, results about a category of Artinian modules over the first Weyl algebra consisting of objects having composition series with composition factors isomorphic to prescribed ones have been obtained. This category corresponds to a tube of Z/2Z type and it is serial and standard. The Auslander-Reiten formula in this category describing the functor Ext(A) (-, -) in terms of the AR-quiver has been derived. The dimensions of Ext(A)(M, N) for M and N in different tubes are calculated.