A few comments on the Clifford algebra \(C\ell_2\) of the standard Euclidean plane
type: Item
instance of: scholarly article
title: A few comments on the Clifford algebra \(C\ell_2\) of the standard Euclidean plane
zbMATH Open document ID: 1277.15016
author: Pierre Anglès
published in: Advances in Applied Clifford Algebras
publication date: 2013-01-10T00:00:00Z
review text: The author studies the structure of the special Clifford algebra \(C\ell_2\) associated with the Euclidean plane. For this reason Clifford mappings are considered. The universal property of \(C\ell_2\) is proved. The geometric achievements of W. K. Clifford are illustrated and explained by carefully chosen examples as for instance the Miquel's theorem. Epistomological remarks enrich the mathematical facts. Clifford's paper on anharmonicity is nicely commented. Of special interest are the explanations on the Clifford-Hopf fibration of \(S^3\) and on the nature of spinors.
Mathematics Subject Classification ID: 15A66
Mathematics Subject Classification ID: 51N15
Mathematics Subject Classification ID: 51N20
Mathematics Subject Classification ID: 01A55
Mathematics Subject Classification ID: 01A60
Mathematics Subject Classification ID: 11E88
zbMATH DE Number: 6123911
zbMATH Keywords: anharmonic
zbMATH Keywords: Alexandrov compactification
zbMATH Keywords: Cauchy plane
zbMATH Keywords: Clifford algebra
zbMATH Keywords: Clifford mapping
zbMATH Keywords: Clifford-Hopf fibration
zbMATH Keywords: cross ratio
zbMATH Keywords: homography
zbMATH Keywords: Miquel's theorem
zbMATH Keywords: spinor
zbMATH Keywords: universal property
MaRDI profile type: Publication
full work available at URL: s00006-012-0346-4
OpenAlex ID: W2031849392
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DOI: 10.1007/S00006-012-0346-4
description: scientific article; zbMATH DE number 6123911