Nambu bracket and M-theory

Abstract

Nambu proposed an extension of dynamical system through the introduction of a new bracket (Nambu bracket) in 1973. This article is a short review of the developments after his paper. Some emphasis are put on a viewpoint that the Nambu bracket naturally describes extended objects which appear in M-theory and the 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 Nambu memorial symposium (Osaka City University, September 29, 2015).

25 pages, contribution to the proceedings of Nambu memorial symposium, Osaka City University, September 29, 2015, v2 minor modifications