Classification of filiform Lie algebras in dimension 8. (Classification des algèbres de Lie filiformes de dimension 8.) (French) Zbl 0628.17005

Ancochea-Bermudez, José Maria; Goze, Michel

Arch. Math. 50, No. 6, 511-525 (1988).

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.

Reviewer: José Maria Ancochea-Bermudez

MSC:

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

Keywords:

classification; complex nilpotent filiform Lie algebras in dimension 8

References:

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