L-infinity Algebra Representation Theory

L_∞ algebras are natural generalizations of Lie algebras from a homotopy theoretical point of view. This concept was originally motivated by a problem in mathematical physics, both as a supporting role in deformation theory and more recently in closed field string theory. Many elementary properties and classical theorems of Lie algebras have been proven to hold true in the homotopy context. Specifically, representation theory of Lie algebras is a subject of current research. Lada and Markl proved the existence of a homotopy theoretic version of Lie algebra representations in the form of L_∞ algebra representations and constructed a one-to-one correspondence between these representations and the homotopy version of Lie modules, L_∞ modules [9]. This dissertation further explores L_∞ modules, highly motivated by classical Lie algebra representation theory.