Deformation theory of infinity algebras

This work explores the deformation theory of algebraic structures in a very general setting. These structures include associative algebras, Lie algebras, and the infinity versions of these structures, the strongly homotopy associative and Lie algebras. In all these cases the algebraic structure is determined by an element of a certain graded Lie algebra which determines a differential on the Lie algebra. We work out the deformation theory in terms of the Lie algebra of coderivations of an appropriate coalgebra structure and construct a universal infinitesimal deformation as well as a miniversal formal deformation. By working at this level of generality, the main ideas involved in deformation theory stand out more clearly. (C) 2002 Elsevier Science (USA). All rights reserved.