Unicity for representations of reduced stated skein algebras
We prove that both stated skein algebras and their reduced versions at odd roots of unity are almost-Azumaya and compute the rank of a reduced stated skein algebra over its center, extending a theorem of Frohman, Kania-Bartoszynska and L\^e to the case of open punctured surfaces. We deduce that gene...
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| creator | Korinman, Julien |
| description | We prove that both stated skein algebras and their reduced versions at odd
roots of unity are almost-Azumaya and compute the rank of a reduced stated
skein algebra over its center, extending a theorem of Frohman,
Kania-Bartoszynska and L\^e to the case of open punctured surfaces. We deduce
that generic irreducible representations of the reduced stated skein algebras
are of quantum Teichm\"uller type and, conversely, that generic quantum
Teichm\"uller type representations are irreducible. |
| doi_str_mv | 10.48550/arxiv.2001.00969 |
| format | Article |
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roots of unity are almost-Azumaya and compute the rank of a reduced stated
skein algebra over its center, extending a theorem of Frohman,
Kania-Bartoszynska and L\^e to the case of open punctured surfaces. We deduce
that generic irreducible representations of the reduced stated skein algebras
are of quantum Teichm\"uller type and, conversely, that generic quantum
Teichm\"uller type representations are irreducible.</description><identifier>DOI: 10.48550/arxiv.2001.00969</identifier><language>eng</language><subject>Mathematics - Algebraic Topology</subject><creationdate>2020-01</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2001.00969$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2001.00969$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Korinman, Julien</creatorcontrib><title>Unicity for representations of reduced stated skein algebras</title><description>We prove that both stated skein algebras and their reduced versions at odd
roots of unity are almost-Azumaya and compute the rank of a reduced stated
skein algebra over its center, extending a theorem of Frohman,
Kania-Bartoszynska and L\^e to the case of open punctured surfaces. We deduce
that generic irreducible representations of the reduced stated skein algebras
are of quantum Teichm\"uller type and, conversely, that generic quantum
Teichm\"uller type representations are irreducible.</description><subject>Mathematics - Algebraic Topology</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2020</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotj8uKwjAYhbNxIToP4GryAq25tEkDbkTmBoIbZ13-JH8kqK0kHdG3n-rM5nxwFofzEbLgrKyaumZLSLd4LQVjvGTMKDMlq-8uujjcaegTTXhJmLEbYIh9l2kfxsr_OPQ0j90DR4wdhdMBbYI8J5MAp4wv_5yR_fvbfvNZbHcfX5v1tgClTREaF4RhDTCsoRHArVbGOhSO45ih0qLiQUmPFisFzksttYWgOVdeaS5n5PVv9nm_vaR4hnRvHxrtU0P-AmTdQ38</recordid><startdate>20200103</startdate><enddate>20200103</enddate><creator>Korinman, Julien</creator><scope>AKZ</scope><scope>GOX</scope></search><sort><creationdate>20200103</creationdate><title>Unicity for representations of reduced stated skein algebras</title><author>Korinman, Julien</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a679-f8cf2908a0e5a82a1b769bce2c1ece2f47241f63debe46acd3737baf7116d6713</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2020</creationdate><topic>Mathematics - Algebraic Topology</topic><toplevel>online_resources</toplevel><creatorcontrib>Korinman, Julien</creatorcontrib><collection>arXiv Mathematics</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Korinman, Julien</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Unicity for representations of reduced stated skein algebras</atitle><date>2020-01-03</date><risdate>2020</risdate><abstract>We prove that both stated skein algebras and their reduced versions at odd
roots of unity are almost-Azumaya and compute the rank of a reduced stated
skein algebra over its center, extending a theorem of Frohman,
Kania-Bartoszynska and L\^e to the case of open punctured surfaces. We deduce
that generic irreducible representations of the reduced stated skein algebras
are of quantum Teichm\"uller type and, conversely, that generic quantum
Teichm\"uller type representations are irreducible.</abstract><doi>10.48550/arxiv.2001.00969</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Algebraic Topology |
| title | Unicity for representations of reduced stated skein algebras |
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