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A Gyrovector Space Approach to Hyperbolic GeometryGyrocommutative Gyrogroups

A Gyrovector Space Approach to Hyperbolic Geometry: Gyrocommutative Gyrogroups [Some gyrocommutative gyrogroups give rise to gyrovector spaces, which are the framework for analytic hyperbolic geometry just as some commutative groups give rise to vector spaces, which are the framework for analytic Euclidean geometry. To pave the way for gyrovector spaces we, therefore, study gyrocommutative gyrogroups in this chapter. In gyrocommutative gyrogroups the gyrogroup operation is gyrocommutative, by Def. 1.8, p. 6, while the gyrogroup cooperation is commutative, by Theorem 2.3 below.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

A Gyrovector Space Approach to Hyperbolic GeometryGyrocommutative Gyrogroups

Part of the Synthesis Lectures on Mathematics & Statistics Book Series
Ungar, Abraham Albert
Springer Journals — Jan 1, 2009
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20 pages

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Publisher
Springer International Publishing
Copyright
© Springer Nature Switzerland AG 2009
ISBN
978-3-031-01268-6
Pages
33 –53
DOI
10.1007/978-3-031-02396-5_2
Publisher site
See Chapter on Publisher Site

Abstract

[Some gyrocommutative gyrogroups give rise to gyrovector spaces, which are the framework for analytic hyperbolic geometry just as some commutative groups give rise to vector spaces, which are the framework for analytic Euclidean geometry. To pave the way for gyrovector spaces we, therefore, study gyrocommutative gyrogroups in this chapter. In gyrocommutative gyrogroups the gyrogroup operation is gyrocommutative, by Def. 1.8, p. 6, while the gyrogroup cooperation is commutative, by Theorem 2.3 below.]

Published: Jan 1, 2009

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