Hom-Lie admissible Hom-coalgebras and Hom-Hopf algebras

The aim of this paper is to generalize the concept of Lie-admissible coalgebra introduced by Goze and Remm to Hom-coalgebras and to introduce Hom-Hopf algebras with some properties. These structures are based on the Hom-algebra structures introduced by the authors.Comment: 13 page

On Koszulity for operads of Conformal Field Theory

We study two closely related operads: the Gelfand-Dorfman operad GD and the Conformal Lie Operad CLie. The latter is the operad governing the Lie conformal algebra structure. We prove Koszulity of the Conformal Lie operad using the Groebner bases theory for operads and an operadic analogue of the Priddy criterion. An example of deformation of an operad coming from the Hom structures is considered. In particular we study possible deformations of the Associative operad from the point of view of the confluence property. Only one deformation, the operad which governs the identity $(\alpha(ab))c=a(\alpha (bc))$ turns out to be confluent. We introduce a new Hom structure, namely Hom--Gelfand-Dorfman algebras and study their basic properties.Comment: 24 page