Deformed Enveloping Algebras

摘要

We construct deformed enveloping algebras without using generators and relations via a generalized semidirect product construction. We give twoHopf algebraic constructions, the first one for general Hopf algebras withtriangular decomposition and the second one for the special case that theouter tensorands are dual. The first construction generalizes Radford'sbiproduct and Majid's double crossproduct, the second one Drinfel'd's Doubleconstruction. The second construction is applied in the last section toconstruct deformed enveloping algebras in the setting created by G. Lusztig.