The Drinfel'd Double Structure Of Generalized Taft Algebras And Their Application To Knot Invariants

Taft algebras are an important class of non-commutative, non-cocommutative Hopf al-gebras, generated by a grouplike element along with a primitive element. In the paper [Hul] published in 2004, Professor Hu Naihong gave the quantized universal enveloping algebra of abelian Lie algebra. For the case when q is a root of unity, it exists a finite dimensional quotient algebra, called the generalized Taft algebra. Our paper will first study the Drin-fel'd double structure of it, and then endow it with some application to knot invariants as quasitriangular Hopf algebra, referring to a series of David Radford's papers published in Journal of Algebra just recent years.