The *-Structure On The Twisted Quantum Double Algebra

In this paper,we study the*-structure on the twisted quantum double algebra D~ω(G).Let G be a finite group,ωbe a normalized 3-cocycle,D~ω(G)=(CG)~*?CG,F be the twist element of D~ω(G),if D~ω(G)admits a*-operation and a element?=(FF~*)~-1,we prove that the new quasi Hopf algebra D_Fω(G)introduced by F is a quasi-Hopf*-algebra when the*-operation and?satisfies certain conditions.Besides,the universal R-matrix of D~ω(G)can induce D~ω(G)to be a quasi-triangular quasi-Hopf*-algebra.