L-Infinity Structures on Spaces with 3 One-Dimensional Components

الأصل · EN

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 Lₙ and L∞ structures on graded vector spaces with three one-dimensional components. In particular, it demonstrates a way to classify ALL possible Lₙ and L∞ structures on V = Vₘ ⊕ Vₘ₊₁ ⊕ Vₘ₊₂ when each of the three components is one-dimensional. Included are necessary and sufficient conditions under which a space with an L₃ structure is a differential graded Lie algebra. It is also shown that some of these d.g. Lie algebras possess a nontrivial Lₙ structure for higher n.