The Nambu bracket and M-theory

Nambu proposed an extension of the dynamical system through the introduction of a new bracket (the Nambu bracket) in 1973. This article is a short review of the developments made since his paper [Phys. Rev. D, 7, 2405 (1973)]. Emphasis is put on the viewpoint that the Nambu bracket naturally describes extended objects that appear in M-theory and fluid dynamics. The latter part of the paper is devoted to a review of the studies on the Nambu bracket (Lie 3-algebra) in Bagger–Lambert–Gustavsson theory of multiple M2-branes. This paper is a contribution to the proceedings of the Nambu Memorial Symposium (Osaka City University, 29 September 2015).