论文标题
部分可观测时空混沌系统的无模型预测
On the structure of abelian Hopf algebras
论文作者
论文摘要
我们研究了完美的特征性$ p $的完美字段$ k $，研究了分级，连接，可计数，交换性和同时性Hopf代数的结构。此类别中的每个$ p $ torsion对象都是明确给定的不可分解的直接总和。这引起了类似的分类，不一定是$ p $ torsion对象，它们要么是自由的，要么是交换代数，要么是无用的cofrave cofosumutative colagebras。我们还完全对那些不可分解的模型$ p $进行分类。
We study the structure of the category of graded, connected, countable-dimensional, commutative and cocommutative Hopf algebras over a perfect field $k$ of characteristic $p$. Every $p$-torsion object in this category is uniquely a direct sum of explicitly given indecomposables. This gives rise to a similar classification of not necessarily $p$-torsion objects that are either free as commutative algebras or cofree as cocommutative coalgebras. We also completely classify those objects that are indecomposable modulo $p$.
