Leonid Makar-Limanov
Wayne University, Detroit, USA
A Bavula's conjecture.
Abstract: Consider a homomorphism \phi of the Weyl algebra A_n into a Weyl algebra A_m. If characteristic of the ground field is zero, then \phi is an embedding since A_n is a simple algebra. If n = 1 then \phi is an embedding in any characteristic because the images of a pair of generators of A_1 should be ``independent". These observation lead Vladimir Bavula to states the following Conjecture:

(BC) Any endomorphism of a Weyl algebra (in a finite characteristic case) is a monomorphism.

In the talk I'll prove BC for A_1, show that BC is wrong for A_n when n > 1, and prove an analogue of BC for the symplectic Poisson algebras.