A conjecture of Bavula on homomorphisms of the Weyl algebra

Details A conjecture of Bavula on homomorphisms of the Weyl algebra A conjecture of Bavula on homomorphisms of the Weyl algebra

2010-04-18

arxiv.org/abs/1004.3028v1

Mathematics

Rings and Algebras

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In the paper {\em 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 $A_1$, show that BC is wrong for $A_n$ when $n > 1$, and prove an analogue of $BC$ for symplectic Poisson algebras.

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