On Integrality of Non-Semisimple Quantum Representations of Mapping Class Groups - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2024

On Integrality of Non-Semisimple Quantum Representations of Mapping Class Groups

Résumé

For a root of unity $ζ$ of odd prime order, we restrict coefficients of non-semisimple quantum representations of mapping class groups associated with the small quantum group $\mathfrak{u}_ζ\mathfrak{sl}_2$ from $\mathbb{Q}(ζ)$ to $\mathbb{Z}[ζ]$. We do this by exhibiting explicit bases of states spaces that span $\mathbb{Z}[ζ]$-lattices that are invariant under projective actions of mapping class groups.
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Dates et versions

hal-04675197 , version 1 (22-08-2024)

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Citer

Marco De Renzi, Jules Martel. On Integrality of Non-Semisimple Quantum Representations of Mapping Class Groups. 2024. ⟨hal-04675197⟩
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