Abstract :
We study conformal algebras from the point of view of conformal dual of classical Lie coalgebra structures. We define the notions of Lie conformal coalgebra and bialgebra. We obtain a conformal analog of the CYBE, the Manin triples and Drinfeldʹs double. With the definition of vertex duals, we obtain a natural description of the Lie algebra associated to a conformal algebra as a convolution algebra, clarifying the classical constructions in the theory of conformal algebras and vertex algebras
