Generalized associative algebras

Loïc Foissy (1)

1 LMPA - Laboratoire de Mathématiques Pures et Appliquées Joseph Liouville

We study diverse parametrized versions of the operad of associative algebra, where the parameter are taken in an associative semigroup Ω (generalization of matching or family associative algebras) or in its cartesian square (two-parameters associative algebras). We give a description of the free algebras on these operads, study their formal series and prove that they are Koszul when the set of parameters is finite. We also study operadic morphisms between the operad of classical associative algebras and these objects, and links with other types of algebras (diassociative, dendriform, post-Lie...).

Mots clés: Family associative algebras; matching associative algebras; two-parameters associative algebras; associative semigroups

Domaines: Anneaux et algèbres [math.RA]

Loïc Foissy. Generalized associative algebras. International Electronic Journal of Algebra, In press. ⟨hal-03187479v3⟩