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Drinfeld doubles of
the $n$-rank Taft algebras and a generalization of the Jones
polynomial
Ge Feng, Naihong Hu and Yunnan Li |
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Vol. 312 (2021), No. 2, 421–456
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Abstract |
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We describe the Drinfeld double structure of the -rank Taft algebra and all of its simple modules, and then endow its -matrices with an application to knot invariants. The knot invariant we get is a generalization of the Jones polynomial, in particular, it coincides with the Jones polynomial in the rank case, while in the rank case, it is the one-parameter specialization of the two-parameter unframed Dubrovnik polynomial, and in higher rank case it is the composite (-power) of the Jones polynomial. |
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Keywords
$n$-rank Taft algebra, Drinfeld double, knot invariants, a
generalization of the Jones polynomial
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Mathematical Subject Classification
Primary: 16T05, 16T25, 17B37, 81R50
Secondary: 57K14, 57K16
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Milestones
Received: 23 November 2020
Revised: 8 March 2021
Accepted: 23 March 2021
Published: 31 August 2021
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Authors |
| Ge Feng | |
| School of Mathematical Sciences and
Shanghai Key Laboratory of PMMP East China Normal University Shanghai 200241 China |
Shanghai Center for Mathematical
Sciences Fudan University Shanghai 200433 China |
| Naihong Hu | |
| School of Mathematical Sciences and
Shanghai Key Laboratory of PMMP East China Normal University Shanghai 200241 China |
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| Yunnan Li | |
| School of Mathematics and
Information Science Guangzhou University Guangzhou 510006 China |
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