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arXiv · 2412.20339

On the formal ribbon extension of a quasitriangular Hopf algebra

Quinn T. Kolt
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Abstract

Any finite-dimensional quasitriangular Hopf algebra $H$ can be formally extended to a ribbon Hopf algebra $\tilde H$ of twice the dimension. We investigate this extension and its representations. We show that every indecomposable $H$-module has precisely two compatible $\tilde H$-actions. We investigate the behavior of simple, projective, and M\"uger central $\tilde H$-modules in terms of these $\tilde H$-actions. We also observe that, in the semisimple case, this construction agrees with the pivotalization/sphericalization construction introduced by Etingof, Nikshych, and Ostrik (2003). As an example, we investigate the formal ribbon extension of odd-index doubled Nichols Hopf algebras $D\mathcal K_n$.

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BibTeXRIS

Quinn T. Kolt. 2024-12-29. On the formal ribbon extension of a quasitriangular Hopf algebra. https://arxiv.org/abs/2412.20339

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