Hypercomplex eight-dimensional nilpotent Lie groups.
type: Item
instance of: scholarly article
title: Hypercomplex eight-dimensional nilpotent Lie groups.
zbMATH Open document ID: 1047.53045
DOI: 10.1016/S0022-4049(03)00104-X
author: I. G. Dotti
author: Anna Fino
published in: Journal of Pure and Applied Algebra
publication date: 2003-09-15T00:00:00Z
review text: 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)].
reviewed by: Marisa Fernández
Mathematics Subject Classification ID: 53C56
Mathematics Subject Classification ID: 53C30
Mathematics Subject Classification ID: 17B30
zbMATH DE Number: 1981483
zbMATH Keywords: nilpotent Lie algebras
zbMATH Keywords: hypercomplex structures
Wikidata QID: Q115340132
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1981483