On an injectivity lemma in the proof of Tannakian duality
Ph\`ung H\^o Hai
TL;DR
This paper presents a concise, elementary proof of the injectivity lemma crucial for Tannakian duality in Hopf algebras and extends it to flat algebras over noetherian domains.
Contribution
It offers a simplified proof of a key lemma in Tannakian duality and generalizes it to broader algebraic contexts.
Findings
Elementary proof of the injectivity lemma
Generalization to flat algebras over noetherian domains
Enhanced understanding of Tannakian duality applications
Abstract
In this short work we give a very short and elementary proof of the injectivity lemma, which plays an important role in the Tannakian duality for Hopf algebras over a field. Based on this we provide some generalizations of this fact to the case of flat algebras over a noetherian domain.
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