A conjecture of Bavula on homomorphisms of the Weyl algebra

الأصل · EN

In the paper The inversion formulae for automorphisms of polynomial algebras and differential operators in prime characteristic, J. Pure Appl. Algebra 212 (2008), no. 10, 2320-2337, see also arXiv:math/0604477, Vladimir Bavula states the following Conjecture: (BC) Any endomorphism of a Weyl algebra (in a finite characteristic case) is a monomorphism. The purpose of this preprint is to prove BC for A₁, show that BC is wrong for Aₙ when n > 1, and prove an analogue of BC for symplectic Poisson algebras.