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Orthogonal Gyrodecompositions of Real Inner Product Gyrogroups
Version 1
: Received: 21 May 2020 / Approved: 23 May 2020 / Online: 23 May 2020 (10:32:43 CEST)
A peer-reviewed article of this Preprint also exists.
Ferreira, M.; Suksumran, T. Orthogonal Gyrodecompositions of Real Inner Product Gyrogroups. Symmetry 2020, 12, 941. Ferreira, M.; Suksumran, T. Orthogonal Gyrodecompositions of Real Inner Product Gyrogroups. Symmetry 2020, 12, 941.
Abstract
In this article, we prove an orthogonal decomposition theorem for real inner product gyrogroups, which unify some well-known gyrogroups in the literature: Einstein, M\"{o}bius, Proper Velocity, and Chen's gyrogroups. This leads to the study of left (right) coset partition of a real inner product gyrogroup induced from a subgyrogroup that is a finite-dimensional subspace. As a result, we obtain gyroprojectors onto the subgyrogroup and its orthogonal complement. We construct also quotient spaces and prove an associated isomorphism theorem. The left (right) cosets are characterized using gyrolines (cogyrolines) together with automorphisms of the subgyrogroup. With the algebraic structure of the decompositions, we study fiber bundles and sections inherited by the gyroprojectors. Finally, the general theory is exemplified for the aforementioned gyrogroups.
Keywords
real inner product gyrogroup; orthogonal decomposition; gyroprojection; coset space; partitions; quotient space; gyrolines; cogyrolines; fiber bundles
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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