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arXiv · 2609.01541

Quantum Hopf rigidity in symmetric monoidal categories

Alexandru Chirvasitu
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Abstract

We prove that a coaction of a Hopf algebra on another preserving the latter's associative-algebra structure and comultiplication automatically also preserves the counit, antipode, and tensor-interchange map and in fact factors through the coaction dual to an action of an affine group scheme by Hopf-algebra automorphisms. This generalizes and unifies a number of results to the effect that quantum groups have only classical symmetries, due to Kasprzak et al., Budziński-Kasprzak and Brannan et al. The stated automatic classicality follows from the fact that the antipode, counit and tensorand-interchange of a Hopf algebra internal to any symmetric monoidal category are contained in the (non-symmetric) monoidal subcategory generated by the associative-algebra structure and the comultiplication, assuming a weak form of arrow-retraction invariance.

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BibTeXRIS

Alexandru Chirvasitu. 2026-09-07. Quantum Hopf rigidity in symmetric monoidal categories. https://arxiv.org/abs/2609.01541

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