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arXiv · 2605.15909

Restricted quantum groups as graded Hopf algebras

Jelena Anić·Giovanni Felder
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Abstract

We introduce the notion of $\pi^2$-graded Hopf algebra, where the grading is by the double groupoid of commutative diagrams of a finite groupoid $\pi$. The finite dimensional representations of a $\pi^2$-graded Hopf algebra form a rigid monoidal category with a fibre functor to the category of $\pi$-graded vector spaces. The main example is given by the restricted quantum groups underlying the Andrews-Baxter-Forrester restricted solid-on-solid models of statistical mechanics and, more generally, the Jimbo-Miwa-Okado models associated to classical Lie algebras.

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Jelena Anić, Giovanni Felder. 2026-05-15. Restricted quantum groups as graded Hopf algebras. https://arxiv.org/abs/2605.15909

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