Hypercomplex eight-dimensional nilpotent Lie groups.
A general classification of nilpotent Lie algebras exists only in dimension \(\leq 7\). In this paper, the authors obtain a description of all \(8\)--dimensional nilpotent Lie algebras with hypercomplex structures. They prove that the existence of a hypercomplex structure implies strong restrictions on the Lie algebra. In fact, its first Betti number is \(\geq 4\). The case when the first Betti number is equal to \(6\) or \(7\), the classification of the corresponding algebras was given by the authors in a previous paper [Ann. Global Anal. Geom. 18, No. 1, 47--59 (2000; Zbl 0945.53031)].
scientific article; zbMATH DE number 1981483