Classical shadows of stated skein representations at roots of unity
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| _version_ | 1866911964254437376 |
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| author | Korinman, Julien Quesney, Alexandre |
| author_facet | Korinman, Julien Quesney, Alexandre |
| contents | We extend some results of Bonahon, Bullock, Turaev and Wong concerning the skein algebras of closed surfaces to L^e's stated skein algebra associated to open surfaces. We prove that the stated skein algebra with deforming parameter +1 embeds canonically into the centers of the stated skein algebras whose deforming parameter is an odd root unity. We also construct an isomorphism between the stated skein algebra at +1 and the algebra of regular function of a generalization of the SL2-character variety of the surface. As a result, we associate to each isomorphism class of irreducible or local representations of the stated skein algebra, an invariant which is a point in the character variety. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1905_03441 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Classical shadows of stated skein representations at roots of unity Korinman, Julien Quesney, Alexandre Geometric Topology Algebraic Topology We extend some results of Bonahon, Bullock, Turaev and Wong concerning the skein algebras of closed surfaces to L^e's stated skein algebra associated to open surfaces. We prove that the stated skein algebra with deforming parameter +1 embeds canonically into the centers of the stated skein algebras whose deforming parameter is an odd root unity. We also construct an isomorphism between the stated skein algebra at +1 and the algebra of regular function of a generalization of the SL2-character variety of the surface. As a result, we associate to each isomorphism class of irreducible or local representations of the stated skein algebra, an invariant which is a point in the character variety. |
| title | Classical shadows of stated skein representations at roots of unity |
| topic | Geometric Topology Algebraic Topology |
| url | https://arxiv.org/abs/1905.03441 |