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arXiv · 2303.13154

Translation Hopf algebras and Hopf heaps

Tomasz Brzeziński·Małgorzata Hryniewicka
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Abstract

To every Hopf heap or quantum cotorsor of Grunspan a Hopf algebra of translations is associated. This translation Hopf algebra acts on the Hopf heap making it a Hopf-Galois co-object. Conversely, any Hopf-Galois co-object has the natural structure of a Hopf heap with the translation Hopf algebra isomorphic to the acting Hopf algebra. It is then shown that this assignment establishes an equivalence between categories of Hopf heaps and Hopf-Galois co-objects.

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Tomasz Brzeziński, Małgorzata Hryniewicka. 2023-03-23. Translation Hopf algebras and Hopf heaps. https://arxiv.org/abs/2303.13154

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