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