Algebra Seminar

A well-known first Weyl algebra A(1) over a field K is generated by two differential operators on K[x], multiplication by x and d/dx. Its simple modules were classified by R.Block in the case of algebraically closed K of characteristic 0. Later the theory has been extended to an arbitrary field. The case of the n-th Weyl algebra A(n)=A(1)×...×A(1) (n times), n>1, is much more difficult. V.Bavula and F.van Oystaeyen used a realization of the algebra A(n) as a "generalized Weyl algebra" in their study of holonomic modules. Following this approach one can obtain a large class of simple and indecomposable modules for an arbitrary field K. Recent results in this direction (joint with V.Bekkert and G.Benkart) will be discussed.

This talk is completely independent of the first talk.