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arXiv · 2103.01081

Drinfel'd doubles of the $n$-rank Taft algebras and a generalization of the Jones polynomial

Ge Feng·Naihong Hu·Yunnan Li
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Abstract

In the paper, we describe the Drinfel'd double structure of the $n$-rank Taft algebra and all of its simple modules, and then endow its $R$-matrices with some application to knot invariants. The knot invariants we get is a generalization of the Jones polynomial, in particular, it recovers the Jones polynomial in rank $1$ case, while in rank $2$ case, it is the one-parameter specialization of the two-parameter unframed Dubrovnik polynomial, and in higher rank case it is the composite ($n$-power) of the Jones polynomial.

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Ge Feng, Naihong Hu, Yunnan Li. 2021-03-01. Drinfel'd doubles of the $n$-rank Taft algebras and a generalization of the Jones polynomial. https://doi.org/10.2140/pjm.2021.312.421

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