Séance Séminaire

Séminaire Algèbre Géométrie Algébrique Topologie Algébrique

Algèbres brace et algèbres B-infini libres

Brace algebras were first introduced by M. Gerstenhaber on the Hochschild cochain complex, in order to describe the so-called Gerstenhaber structure on the Hochschild homology of an algebra. We obtain an easy description for free braces algebras, and show in a very easy way a result of Lada and Markl which states that symmetric brace algebras are pre-Lie algebras. In a similar way, we use the construction of free 2-associative aslgebras to recover the free objects for B-infinity algebras, which are a generalization of brace algebras, related to deformation theory. We give an easy example of analgebra, equipped with two non-isomorphic structures of B-infinity algebra which give the same Hopf algebra structure.