The *-operation And Duality In Twisted Drinfeld Double Algebra

Given a finite group G and a three-cocycle ω∈H3(G,U(1))the twisted Drinfeld double Dω(G)can be defined to be the algebra over the complex numbers.F is the field algebra of G-spin models.There is a*-operation so thatDω(G)is a Hopf C*-algebra when G is abelian.At this point,there is a C*-representation of Dω(G)so that Dω(G)and AG are commutants of each other where AG is the Dω(G)-invariant space.