The Hopf algebroid structure of differentially recursive sequences
The Hopf algebroid structure of differentially recursive sequences
复制标题
微分递归序列的Hopf代数体结构
DOI：
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
P. Saracco
中科院分区：
文献类型：
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作者：
L. Kaoutit;P. Saracco
微分域上的微分递归序列是Hurwitz级数微分代数中满足一个变系数齐次微分方程（即域元素的Taylor展开式）的元素序列。本文的主要目的是研究域上具有非零微分的所有微分递归序列的空间。我们表明，这些序列形成一个双边的向量空间，承认，在一个典型的方式，结构的Hopf代数体上的常元素的子域。我们证明了它是线性微分方程形式解空间的直接极限，作为左余模，并且它作为Hopf代数体满足一个附加的普适性质.当基域上的微分为零时，我们恢复了线性递归序列的Hopf代数结构。
Abstract A differentially recursive sequence over a differential field is a sequence of elements satisfying a homogeneous differential equation with non-constant coefficients (namely, Taylor expansions of elements of the field) in the differential algebra of Hurwitz series. The main aim of this paper is to explore the space of all differentially recursive sequences over a given field with a non-zero differential. We show that these sequences form a two-sided vector space that admits, in a canonical way, a structure of Hopf algebroid over the subfield of constant elements. We prove that it is the direct limit, as a left comodule, of all spaces of formal solutions of linear differential equations and that it satisfies, as Hopf algebroid, an additional universal property. When the differential on the base field is zero, we recover the Hopf algebra structure of linearly recursive sequences.