Abstract
L ∞ 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 ∞ structures on graded vector spaces with three one-dimensional components. In particular, it demonstrates a way to classify all possible L n and L ∞ structures on V = V m ⊕ V m+1 ⊕ V m+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.
Acknowledgments
The results in this paper are a portion of my Ph.D. research under the supervision of Tom Lada. I would also like to thank Jim Stasheff for many helpful suggestions and comments.
Notes
#Communicated by K. Misra.