On the dimensions of automorphism groups of eight-dimensional ternary fields. II
type: Item
instance of: scholarly article
title: On the dimensions of automorphism groups of eight-dimensional ternary fields. II
zbMATH Open document ID: 0829.51007
DOI: 10.1007/BF01264022
author: Richard Bödi
published in: Geometriae Dedicata
publication date: 1995-02-26T00:00:00Z
review text: The automorphism group of a ternary field is naturally isomorphic to the stabilizer of a quadrangle in the collineation group of the corresponding projective plane. Consideration of compact projective planes of topological dimension 16 (these planes are relatives of the octonion plane) leads to locally compact ternary fields of topological dimension 8. Let \(\Gamma\) be the automorphism group of such a ternary field. The author proves that \(\Gamma\) is isomorphic to one of the compact groups \(G_2\) or \(\text{SU}_3 \mathbb{C}\), or \(\Gamma\) has topological dimension at most 7; actually, he obtains much more detailed information about \(\Gamma\). The proof is rather involved, by necessity, because at present it is not known if \(\Gamma\) is always compact, or a Lie group. [Part I has appeared in J. Geom. 52, No. 1-2, 30-40 (1995; see the review above)].
Mathematics Subject Classification ID: 51H10
Mathematics Subject Classification ID: 22A30
Mathematics Subject Classification ID: 51A10
Mathematics Subject Classification ID: 51A35
Mathematics Subject Classification ID: 12J99
zbMATH DE Number: 727305
zbMATH Keywords: automorphism group
zbMATH Keywords: ternary field
reviewed by: Theo Grundhöfer
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01264022
OpenAlex ID: W3140389208
description: scientific article; zbMATH DE number 727305