Quasi-Hopf Algebra

A quasi-Hopf algebra is a generalization of a Hopf algebra, which was defined by the Russian mathematician Vladimir Drinfeld in 1989.

A quasi-Hopf algebra is a quasi-bialgebra for which there exist and a bijective antihomomorphism S (antipode) of such that

for all and where

and

where the expansions for the quantities and are given by

and

As for a quasi-bialgebra, the property of being quasi-Hopf is preserved under twisting.