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arXiv · 1004.3028

A conjecture of Bavula on homomorphisms of the Weyl algebra

Leonid Makar-Limanov
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Abstract

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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Leonid Makar-Limanov. 2010-04-18. A conjecture of Bavula on homomorphisms of the Weyl algebra. https://arxiv.org/abs/1004.3028

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