Cogebres Lie-admissibles - Lie-admissible coalgebras

We present coalgebras of some classes of nonassociative algebras whose associator satisfies invariance conditions given by the action of the 3-order symmetric group. Amongst these algebras we find the well-known Vinberg algebras, the Pre-Lie algebras, the Lie-admissible algebras and the 3-power associative algebras. We study properties between these coalgebras and algebras which generalize the associative case.