Bivariate Dimension polynomials and New Invariants of Finitely Generated d-Modules
Bivariate Dimension polynomials and New Invariants of Finitely Generated d-Modules
复制标题
双变量维多项式和有限生成 d 模的新不变量
DOI：
--
复制
发表时间：
2013
影响因子：
0.8
通讯作者：
A. Levin
中科院分区：
文献类型：
--
作者：
Christian Dönch;A. Levin
本文推广了经典的Grobner基技术，证明了有限生成d模（即Weyl代数上的有限生成模）的二变量维多项式的存在性，并给出了一种计算方法。我们还给出了相应的算法和计算实例，并证明了二元维多项式包含d模的不变量，这些不变量不包含在它的Bernstein维多项式中。然后将所得结果应用于d模的同构问题。
In this paper, we generalize the classical Grobner basis technique to prove the existence and present a method of computation of a dimension polynomial in two variables associated with a finitely generated D-module, that is, a finitely generated module over a Weyl algebra. We also present corresponding algorithms and examples of computation of such polynomials and show that bivariate dimension polynomials contain invariants of a D-module, which are not carried by its Bernstein dimension polynomial. Then we apply the obtained results to the isomorphism problem for D-modules.