Orthochronous Lorentz group from the Cliffordian point of view
type: Item
instance of: scholarly article
title: Orthochronous Lorentz group from the Cliffordian point of view
zbMATH Open document ID: 0893.20034
author: Pierrick Meignen
published in: Advances in Applied Clifford Algebras
publication date: 1998-08-24T00:00:00Z
review text: Using the Lorentz quadratic form \(q\) on \(\mathbb{R}^n\) of signature \((n-1,1)\), the orthochronous (future preserving half of) Lorentz group \(O^+(n-1,1)\), forms the full isometry group of the model of hyperbolic space \(\mathbb{H}^{n-1}\), formed by the projective image of the positive cone \(C=\{x\in\mathbb{R}^n\mid q(x,x)<0,\;x_n>0\}\). Alternatively, in the upper half space model of \(\mathbb{H}^{n-1}\) the full isometry group can be described by the action of certain \(2\times 2\) matrices with entries in the Clifford group generated by vectors in a suitably defined Clifford algebra. In this paper, very explicit descriptions are obtained, at the level of elements, between these two representations of this isometry group.
Mathematics Subject Classification ID: 20G20
Mathematics Subject Classification ID: 22E43
Mathematics Subject Classification ID: 15A66
zbMATH DE Number: 1045723
zbMATH Keywords: orthochronous Lorentz group
zbMATH Keywords: Lorentz quadratic forms
zbMATH Keywords: isometry groups
zbMATH Keywords: hyperbolic spaces
zbMATH Keywords: Clifford algebras
reviewed by: C. Maclachlan
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1045723