On the formal ribbon extension of a quasitriangular Hopf algebra
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915199575916544 |
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| author | Kolt, Quinn T. |
| author_facet | Kolt, Quinn T. |
| contents | 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 Müger 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 $D\mathcal K_n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20339 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the formal ribbon extension of a quasitriangular Hopf algebra Kolt, Quinn T. Quantum Algebra Rings and Algebras Representation Theory 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 Müger 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 $D\mathcal K_n$. |
| title | On the formal ribbon extension of a quasitriangular Hopf algebra |
| topic | Quantum Algebra Rings and Algebras Representation Theory |
| url | https://arxiv.org/abs/2412.20339 |