Dual Lie bialgebra structures of loop and current Virasoro\\ algebras

The loop and current Virasoro algebras are respectively the tensor product Lie algebras of the Virasoro algebra with the polynomial and Laurent polynomial algebra. In the present paper, the structures of dual Lie bialgebras of loop and current Virasoro algebras are investigated. As a result, a series of new infinite dimensional Lie algebras are obtained.