The deformation complex is a homotopy invariant of a homotopy algebra

Abstract

To a homotopy algebra one may associate its deformation complex, which is naturally a differential graded Lie algebra. We show that infinity quasi-isomorphic homotopy algebras have L-infinity quasi-isomorphic deformation complexes by an explicit construction.Comment: A revised version. The final version will appear in the volume "Current Developments and Retrospectives in Lie Theory