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VOL. 17 | 2016 On the Geometry Induced by Lorentz Transformations in Pseudo-Euclidean Spaces
Abraham Ungar

Editor(s) Ivaïlo M. Mladenov, Guowu Meng, Akira Yoshioka

## Abstract

The Lorentz transformations of order $(m,n)$ in pseudo-Euclidean spaces with indefinite inner product of signature $(m,n)$ are extended in this work from $m=1$ and $n\ge1$ to all $m,n\ge1$. A parametric realization of the Lorentz transformation group of any order $(m,n)$ is presented, giving rise to generalized gyrogroups and gyrovector spaces called bi-gyrogroups and bi-gyrovector spaces. The latter, in turn, form the setting for generalized analytic hyperbolic geometry that underlies generalized balls called eigenballs.

## Information

Published: 1 January 2016
First available in Project Euclid: 15 December 2015

zbMATH: 1346.83006
MathSciNet: MR3445441

Digital Object Identifier: 10.7546/giq-17-2016-360-368