关于Weyl代数同态的Bavula猜想
A conjecture of Bavula on homomorphisms of the Weyl algebra
摘要：
在论文{ \em The inversion formulas for automorphisms of polynomial algebras and微分算子in prime characteristic}，J. Pure Appl. Algebra 212（2008），no. 10，2320-2337，也参见arXiv：math/0604477，Vladimir Bavula陈述了以下猜想：（BC）Weyl代数的任何自同态（在有限特征情况下）是单态。这个预印本的目的是证明BC对于$A_1$，证明BC对于$A_n$在$n > 1$时是错误的，并证明$BC$对于辛Poisson代数的一个模拟。
英文摘要：
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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