L∞ structures on spaces with three one-dimensional components

L-infinity structures have been a subject of recent interest in physics, where they occur in closed string theory and in gauge theory. This paper provides a class of easily constructible examples of L-n and L-infinity structures on graded vector spaces with three one-dimensional components. In particular, it demonstrates a way to classify all possible L-n and L-infinity structures on V = V-m circle plus Vm+1 circle plus Vm+2 when each of the three components is one-dimensional. Included are necessary and sufficient conditions under which a space with an L-3 structure is a differential graded Lie algebra. It is also shown that some of these differential graded Lie algebras possess a nontrivial L-n structure for higher n.