Strong Homotopy Lie Algebras, Generalized Nahm Equations and Multiple M2-branes
High Energy Physics - Theory
2009-01-27 v1
Abstract
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.
Keywords
Cite
@article{arxiv.0901.3905,
title = {Strong Homotopy Lie Algebras, Generalized Nahm Equations and Multiple M2-branes},
author = {Calin I. Lazaroiu and Daniel McNamee and Christian Saemann and Aleksandar Zejak},
journal= {arXiv preprint arXiv:0901.3905},
year = {2009}
}
Comments
1+28 pages