Examples of Homotopy Lie Algebras
arXiv:0903.5433
Abstract
We look at two examples of homotopy Lie algebras (also known as L_{\infty} algebras) in detail from two points of view. We will exhibit the algebraic point of view in which the generalized Jacobi expressions are verified by using degree arguments and combinatorics. A second approach using the nilpotency of Grassmann-odd differential operators Δto verify the homotopy Lie data is shown to produce the same results.
12 pages, LaTeX. v2: Minor corrections. To appear in the proceedings of the 29th Srni winter school "Geometry and Physics", published in the journal Archivum Mathematicum (Brno), see http://emis.muni.cz/journals/AM/