Journal of Lie Theory, Vol. 10, No. 1, pp. 181-194 (2000)

Nambu-Lie Groups

Izu Vaisman

Department of Mathematics
University of Haifa
Haifa 31905, Israel

Abstract: We extend the Nambu bracket to $1$-forms. Following the Poisson-Lie case, we define Nambu-Lie groups as Lie groups endowed with a multiplicative Nambu structure. A Lie group $G$ with a Nambu structure $P$ is a Nambu-Lie group iff $P=0$ at the unit, and the Nambu bracket of left (right) invariant forms is left (right) invariant. We define a corresponding notion of a Nambu-Lie algebra. We give several examples of Nambu-Lie groups and algebras.

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