Free product of operads and free basis of Lie-admissible operad

Abstract

In this paper, we introduce the definition of free product of operads, following the definition of a free product of algebras. There is a given method of finding the basis and dimension of the free product of operads. By anti-commutative operation, Lie-admissible algebra gives Lie algebra. We proved that Lie-admissible operad isomorphic to the free product of Lie and commutative(non-associative) operads.