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On Filippov algebroids and multiplicative Nambu-Poisson structures

Abstract

We discuss relations between linear Nambu-Poisson structures and Filippov algebras and define Filippov algebroids which are n-ary generalizations of Lie algebroids. We also prove results describing multiplicative Nambu- Poisson structures on Lie groups. In particular, we show that simple Lie groups do not admit multiplicative Nambu-Poisson structures of order n>2.Comment: Latex, 22 pages, to appear in Diff. Geom. App

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