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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.

##### MSC:
 17B30 Solvable, nilpotent (super)algebras
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##### References:
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