论文标题
差异递归序列的HOPF代数结构
The Hopf algebroid structure of differentially recursive sequences
论文作者
论文摘要
在差分场上的差递归序列是一系列元素，这些元素满足具有非恒定系数的均质微分方程（即，田间元素的泰勒（Taylor of Taylor）系列元素的扩展）。本文的主要目的是探索具有非零差分的给定场上所有差异递归序列的空间。我们表明，这些序列形成了一个双面矢量空间，该空间以规范的方式接受了恒定元素子场的Hopf代数的结构。我们证明，作为线性微分方程的正式解决方案的所有空间，这是直接限制，并且像Hopf Algebroid一样满足了额外的通用属性。当基础场上的差分为零时，我们恢复线性递归序列的HOPF代数结构。
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.
