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Classification of filiform Lie algebras in dimension 8. (Classification des algèbres de Lie filiformes de dimension 8.) (French) Zbl 0628.17005
We give the classification of complex nilpotent filiform Lie algebras in dimension 8. Recall that an \(n\)-dimensional nilpotent Lie algebra \(\mathfrak g\) is filiform if there is a vector \(X\) in \(\mathfrak g\) and a basis \((X,X_ 2,\ldots,X_ n)\) such that \((\text{ad}\, X)(X_ i)=X_{i-1}\), \(i=3,\ldots,n\). We prove that we have a filiform 8-dimensional Lie algebra whose orbit is open in the manifold of the 8-dimensional nilpotent Lie algebra structure.

17B30 Solvable, nilpotent (super)algebras
17B05 Structure theory for Lie algebras and superalgebras
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