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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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