Representations of finite-dimensional quotient algebras of the 3-string braid group
We consider quotients of the group algebra of the $3$-string braid group $B_3$ by $p$-th order generic polynomial relations on the elementary braids. In cases $p=2,3,4,5$ these quotient algebras are finite dimensional. We give semisimplicity criteria for these algebras and present explicit formulas...
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| creator | Pyatov, Pavel Trofimova, Anastasia |
| description | We consider quotients of the group algebra of the $3$-string braid group
$B_3$ by $p$-th order generic polynomial relations on the elementary braids. In
cases $p=2,3,4,5$ these quotient algebras are finite dimensional. We give
semisimplicity criteria for these algebras and present explicit formulas for
all their irreducible representations. |
| doi_str_mv | 10.48550/arxiv.1808.06395 |
| format | Article |
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$B_3$ by $p$-th order generic polynomial relations on the elementary braids. In
cases $p=2,3,4,5$ these quotient algebras are finite dimensional. We give
semisimplicity criteria for these algebras and present explicit formulas for
all their irreducible representations.</description><identifier>DOI: 10.48550/arxiv.1808.06395</identifier><language>eng</language><subject>Mathematics - Mathematical Physics ; Mathematics - Quantum Algebra ; Mathematics - Representation Theory ; Physics - Mathematical Physics</subject><creationdate>2018-08</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/1808.06395$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1808.06395$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Pyatov, Pavel</creatorcontrib><creatorcontrib>Trofimova, Anastasia</creatorcontrib><title>Representations of finite-dimensional quotient algebras of the 3-string braid group</title><description>We consider quotients of the group algebra of the $3$-string braid group
$B_3$ by $p$-th order generic polynomial relations on the elementary braids. In
cases $p=2,3,4,5$ these quotient algebras are finite dimensional. We give
semisimplicity criteria for these algebras and present explicit formulas for
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$B_3$ by $p$-th order generic polynomial relations on the elementary braids. In
cases $p=2,3,4,5$ these quotient algebras are finite dimensional. We give
semisimplicity criteria for these algebras and present explicit formulas for
all their irreducible representations.</abstract><doi>10.48550/arxiv.1808.06395</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Mathematical Physics Mathematics - Quantum Algebra Mathematics - Representation Theory Physics - Mathematical Physics |
| title | Representations of finite-dimensional quotient algebras of the 3-string braid group |
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