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On the \(k\)-abelian filiform Lie algebras. (English) Zbl 0866.17009
The authors consider complex filiform Lie algebras with \(C^k(L)\) abelian where \(C^0(L)=L\) and \(C^{k+1}(L)= [C^k(L),L]\). A complete classification is obtained when \(k=2\). This classification divides into 17 cases and it is determined that, except in a few cases, the algebras are not isomorphic. It is also observed that, except in a few cases, the algebras are characteristically nilpotent.

17B30 Solvable, nilpotent (super)algebras
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