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 generalization of a Hopf algebra, which was defined by the Russian mathematician Vladimir Drinfeld in 1989. A quasi-Hopf algebra is a quasi-bialgebra B A = ( A , Δ , ε , Φ ) {displaystyle {mathcal {B_{A}}}=({mathcal {A}},Delta ,varepsilon ,Phi )} for which there exist α , β ∈ A {displaystyle alpha ,eta in {mathcal {A}}} and a bijective antihomomorphism S (antipode) of A {displaystyle {mathcal {A}}} such that for all a ∈ A {displaystyle ain {mathcal {A}}} and where