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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].

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