A characterization of finite dimensional nilpotent Filippov algebras

Abstract

Let A be a nilpotent Filippov ( n -Lie) algebra of dimension d and put s ( A ) = ( d − 1 n ) + n − 1 − dim M ( A ) and t ( A ) = ( d n ) − dim M ( A ) , where M ( A ) denotes the multiplier of A . The aim of this paper is to classify all nilpotent n -Lie algebras A for which s ( A ) = 0 , 1 or 2, and apply it in order to determine all nilpotent n -Lie algebras A satisfying 0 ≤ t ( A ) ≤ 8 .