Endomorphisms of Weyl algebra and $p$-curvatures
Endomorphisms of Weyl algebra and $p$-curvatures
复制标题
DOI：
10.18910/7472
复制
发表时间：
2005-06
影响因子：
0.4
通讯作者：
Yoshifumi Tsuchimoto
中科院分区：
文献类型：
--
作者：
Yoshifumi Tsuchimoto
We first show that for each Weyl algebra over a positive charac te istic field, we may obtain an affine space with a projectively flat connection on it. We give a set of differential equations which controls the behavior of th e connection under endomorphism of the Weyl algebra. The key is the theory of -curvat ures. Next we introduce a fieldQ( ) U of characteristic zero as a limit of fields of positive characteristics. We need to fix an ultrafilter on the set of prime numbers to do this. The field is actually isomorphic to the field C of complex numbers. Then we show that we may associate with a Weyl algebra over the field Q( ) U an affine space with a symplectic form in a functorial way. Tha t means, the association is done in such a way that an endomorphism of the Weyl a lgebra induces a symplectic map of the affine space. As a result, we show that a solution of the Jacobian conjectur is sufficient for an affirmative answer to the Dixmier conjecture.
