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Family of \(p\)-filiform Lie algebras. (English) Zbl 0924.17005
Khakimdjanov, Yusupdjan (ed.) et al., Algebra and operator theory. Proceedings of the colloquium, Tashkent, Uzbekistan, September 29–October 5, 1997. Dordrecht: Kluwer Academic Publishers. 93-102 (1998).
Several partial results were obtained until now in connection with the classification problem of the finite-dimensional nilpotent Lie algebras. Most of the approaches are concerned with “low-dimensional” algebras and are based on the notion of characteristic sequence, introduced by J. M. Ancochea-Bermudez and M. Goze [C. R. Acad. Sci., Paris, Sér. I 302, 611-613 (1986; Zbl 0591.17008)].
In the paper under review one studies the classification of the finite-dimensional (real or complex) nilpotent Lie algebras belonging to certain classes having arbitrary dimension. One introduces first the \(p\)-filiform algebras: a nilpotent Lie algebra \(g\) is called \(p\)-filiform if its characteristic sequence equals \((\dim g-p,1,1,\dots,1)\). Then the paper provides an explicit (and detailed) classification of the \(p\)-filiform Lie algebras \(g\) with \(p\in\{\dim g-1, \dim g-2, \dim g-3\}\).
For the entire collection see [Zbl 0908.00015].

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