  We review various generalizations of the notion of Lie algebras, in
particular those appearing in the recently proposed Bagger-Lambert-Gustavsson
model, and study their interrelations. We find that Filippov's n-Lie algebras
are a special case of strong homotopy Lie algebras. Furthermore, we define a
class of homotopy Maurer-Cartan equations, which contains both the Nahm and the
Basu-Harvey equations as special cases. Finally, we show how the super
Yang-Mills equations describing a Dp-brane and the Bagger-Lambert-Gustavsson
equations supposedly describing M2-branes can be rewritten as homotopy
Maurer-Cartan equations, as well.
