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In the paper, we describe the Drinfel'd double structure of the $n$-rank Taftalgebra and all of its simple modules, and then endow its $R$-matrices withsome application to knot invariants. The knot invariants we get is ageneralization of the Jones polynomial, in particular, it recovers the Jonespolynomial in rank $1$ case, while in rank $2$ case, it is the one-parameterspecialization of the two-parameter unframed Dubrovnik polynomial, and inhigher rank case it is the composite ($n$-power) of the Jones polynomial.

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