On the structure of abelian Hopf algebras

Tilman Bauer

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arXiv · 2203.01676

On the structure of abelian Hopf algebras

Tilman Bauer

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Abstract

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 $p$.

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Tilman Bauer. 2022-03-03. On the structure of abelian Hopf algebras. https://arxiv.org/abs/2203.01676

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