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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Funding
This research was partially supported by the National Science Centre, Poland, grant no. 2019/35/B/ST1/01115. The research of Tomasz Brzeziński is partially supported by the National Science Centre, Poland WEAVE-UNISONO grant 2023/05/Y/ST1/00046.
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Tomasz Brzeziñski and Malgorzata Hryniewicka contributed equally at all stages of preparation - including the revisions - of this manuscript. In addition, Tomasz Brzeziñski is handling the submission as the corresponding author.
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Presented by: Milen Yakimov
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Brzeziński, T., Hryniewicka, M. Translation Hopf Algebras and Hopf Heaps. Algebr Represent Theor (2024). https://doi.org/10.1007/s10468-024-10283-9
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DOI: https://doi.org/10.1007/s10468-024-10283-9