Fundamental theorem of projective geometry in Lie modules and algebras
type: Item
instance of: scholarly article
title: Fundamental theorem of projective geometry in Lie modules and algebras
zbMATH Open document ID: 0728.51003
DOI: 10.1007/BF01094423
author: Alexander Lashkhi
published in: Journal of Soviet Mathematics
publication date: 1988-01-01T00:00:00Z
review text: Es ist wohlbekannt, daß jeder Automorphismus eines projektiven Raumes über einem Schiefkörper K (oder des zugehörigen Unterraumverbandes) durch eine semilineare Abbildung des zugehörigen K-Vektorraumes X induziert werden kann (Hauptsatz der projektiven Geometrie). Verf. untersucht Verallgemeinerungen dieses Sachverhaltes, indem er schwächere Bedingungen für K und X verlangt. So bleibt der Hauptsatz gültig, wenn K ein kommutativer Ring mit 1 und X frei über K ist. Entsprechendes gilt im wesentlichen auch für Linkshauptidealringe. Im weiteren Verlauf untersucht Verf. den Fall, daß K eine Lie-Algebra über einem kommutativen Hauptidealring ist. Der Hauptsatz gilt z.B., wenn K eine reine lokal nilpotente oder eine freie Lie-Algebra ist.
Mathematics Subject Classification ID: 51A05
Mathematics Subject Classification ID: 17B99
Mathematics Subject Classification ID: 16D99
zbMATH DE Number: 4203148
zbMATH Keywords: fundamental theorem of projective geometry
zbMATH Keywords: collineations
zbMATH Keywords: lattice isomorphisms
zbMATH Keywords: Lie algebra over commutative principal ideal rings
reviewed by: Johannes André
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4203148