Non-commutative affine kinematic spaces and their automorphism group
type: Item
instance of: scholarly article
title: Non-commutative affine kinematic spaces and their automorphism group
zbMATH Open document ID: 0636.51013
DOI: 10.1007/BF03322404
author: Silvia Pianta
published in: Results in Mathematics
publication date: 1987-01-01T00:00:00Z
review text: As \textit{H. Karzel} and \textit{G. Kist} showed [J. Geom. 23, 124-127 (1984; Zbl 0558.51014)], any noncommutative pappian affine kinematic space can be described with the help of a near vector space. To investigate the automorphism groups of these kinematic spaces the author defines near- semilinear maps, namely maps between near vector spaces with the properties of semilinear maps. She shows that the set of automophisms of a noncommutative affine kinematic space is the group of all bijective near-semilinear maps of the belonging near vector space. For the special case of dimension 3 one gets that this groups is the semidirect product of the group of inner automorphisms with a product of linear maps and field automorphisms.
Mathematics Subject Classification ID: 51J15
Mathematics Subject Classification ID: 51J20
zbMATH DE Number: 4036596
zbMATH Keywords: kinematic algebra
zbMATH Keywords: automorphism group
zbMATH Keywords: near vector spaces
zbMATH Keywords: kinematic space
reviewed by: Herbert Hotje
MaRDI profile type: Publication
cites work: Q5185242
cites work: Q4771790
cites work: Determination of all near vector spaces with projective and affine fibrations
cites work: Q5682875
cites work: Zur Darstellung zweiseitiger affiner Inzidenzgruppen
description: scientific article; zbMATH DE number 4036596