Möbius gyrogroups: a Clifford algebra approach.
type: Item
instance of: scholarly article
title: Möbius gyrogroups: a Clifford algebra approach.
zbMATH Open document ID: 1246.20062
author: Yong-Cai Geng
author: Sumit K. Garg
published in: Journal of Algebra
publication date: 2011-05-16T00:00:00Z
full work available at URL: http://hdl.handle.net/10400.8/3817
review text: This article continues the investigations of the first author [in Adv. Appl. Clifford Algebr. 19, No. 2, 303-323 (2009; Zbl 1197.20056)] restricting the interest to the finite dimensional case and giving more details. In particular they use their results to study the sections of Möbius fiber bundles inherited by the Möbius projectors. For more details we refer the reader to the authors' summary: ``Using the Clifford algebra formalism we study the Möbius gyrogroup of the ball of radius \(t\) of the paravector space \(\mathbb R\oplus V\), where \(V\) is a finite-dimensional real vector space. We characterize all the gyro-subgroups of the Möbius gyrogroup and we construct left and right factorizations with respect to an arbitrary gyro-subgroup for the paravector ball. The geometric and algebraic properties of the equivalence classes are investigated. We show that the equivalence classes locate in a \(k\)-dimensional sphere, where \(k\) is the dimension of the gyro-subgroup, and the resulting quotient spaces are again Möbius gyrogroups.''
Mathematics Subject Classification ID: 20N05
Mathematics Subject Classification ID: 11E88
Mathematics Subject Classification ID: 15A66
Mathematics Subject Classification ID: 83A05
Mathematics Subject Classification ID: 53A60
Mathematics Subject Classification ID: 30G35
Mathematics Subject Classification ID: 22E43
Mathematics Subject Classification ID: 18A32
zbMATH DE Number: 5888491
zbMATH Keywords: Möbius gyrogroups
zbMATH Keywords: Möbius projectors
zbMATH Keywords: finite-dimensional real Clifford algebras
zbMATH Keywords: Möbius fiber bundles
reviewed by: Liudmila Sabinina
MaRDI profile type: Publication
OpenAlex ID: W2047279941
cites work: Q3665386
cites work: Möbius transformations in expressed through 2×2 matrices of clifford numbers
cites work: Q4003806
cites work: Spherical continuous wavelet transforms arising from sections of the Lorentz group
cites work: Factorizations of Möbius gyrogroups.
cites work: Strong near subgroups and left gyrogroups
cites work: Gyrogroups and the decomposition of groups into twisted subgroups and subgroups.
cites work: Physical applications of homogeneous balls. With the assistance of Tzvi Scarr
cites work: Why does the geometric product simplify the equations of physics?
cites work: Q3995205
cites work: Q3937844
cites work: Q5715578
cites work: Q5433130
cites work: From Möbius to Gyrogroups
cites work: Extension of the unit disk gyrogroup into the unit ball of any real inner product space
cites work: Möbius transformations of the ball, Ahlfors' rotation and gyrovector spaces.
cites work: Möbius transformations in several dimensions
DOI: 10.1016/J.JALGEBRA.2010.05.014
description: scientific article; zbMATH DE number 5888491