Proceedings of the International Conference on Geometry, Integrability and Quantization

On the Geometry Induced by Lorentz Transformations in Pseudo-Euclidean Spaces

Abraham Ungar

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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.

Article information

Source
Proceedings of the Seventeenth International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov, Guowu Meng and Akira Yoshioka, eds. (Sofia: Avangard Prima, 2016), 360-368

Dates
First available in Project Euclid: 15 December 2015

Permanent link to this document
https://projecteuclid.org/ euclid.pgiq/1450194168

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

Mathematical Reviews number (MathSciNet)
MR3445441

Zentralblatt MATH identifier
1346.83006

Citation

Ungar, Abraham. On the Geometry Induced by Lorentz Transformations in Pseudo-Euclidean Spaces. Proceedings of the Seventeenth International Conference on Geometry, Integrability and Quantization, 360--368, Avangard Prima, Sofia, Bulgaria, 2016. doi:10.7546/giq-17-2016-360-368. https://projecteuclid.org/euclid.pgiq/1450194168


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