  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.
