On Filippov algebroids and multiplicative Nambu-Poisson structures
Janusz Grabowski, Giuseppe Marmo
TL;DR
This paper explores the connection between Filippov algebroids and Nambu-Poisson structures, introduces Filippov algebroids as n-ary generalizations of Lie algebroids, and characterizes multiplicative Nambu-Poisson structures on Lie groups.
Contribution
It defines Filippov algebroids and proves that simple Lie groups cannot have multiplicative Nambu-Poisson structures of order greater than two.
Findings
Filippov algebroids are n-ary generalizations of Lie algebroids.
Simple Lie groups do not admit multiplicative Nambu-Poisson structures of order n>2.
Relations between linear Nambu-Poisson structures and Filippov algebras are established.
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.
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Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models