Affine structures on 4-step nilpotent Lie algebras
type: Item
instance of: scholarly article
title: Affine structures on 4-step nilpotent Lie algebras
zbMATH Open document ID: 0909.17009
DOI: 10.1016/S0022-4049(96)00057-6
author: Karel Dekimpe
author: Manfred Hartl
published in: Journal of Pure and Applied Algebra
publication date: 1999-04-08T00:00:00Z
review text: The authors introduce a new method for constructing minimal affine representations of Lie algebras. This method, using polynomial constructions, relates to one in group theory developed by \textit{I. B. S. Passi} [J. Algebra 16, 121-151 (1968; Zbl 0159.31502)]. In particular, for certain nilpotent Lie algebras of class-4, modules are constructed which show the existence of complete left-symmetric structures and minimal faithful affine representations. This construction has bearing on the problem of groups being realized as fundamental groups of compact, complete affinely flat manifolds [cf. \textit{J. Milnor}, Adv. Math. 25, 178-187 (1977; Zbl 0364.55001)].
Mathematics Subject Classification ID: 17B15
Mathematics Subject Classification ID: 17B30
zbMATH DE Number: 1061803
zbMATH Keywords: minimal affine representations
zbMATH Keywords: polynomial constructions
zbMATH Keywords: nilpotent Lie algebras of class-4
zbMATH Keywords: complete left-symmetric structures
zbMATH Keywords: minimal faithful affine representations
Wikidata QID: Q115340124
reviewed by: Ernest L. Stitzinger
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1061803