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Title: Orthogonal gyrodecompositions of real inner product gyrogroups
Author: Ferreira, Milton
Suksumran, Teerapong
Keywords: Real inner product gyrogroup
Orthogonal decomposition
Coset space
Quotient space
Fiber bundles
Issue Date: Jun-2020
Publisher: MDPI
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, Möbius, 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.
Peer review: yes
DOI: 10.3390/sym12060941
ISSN: 2073-8994
Publisher Version:
Appears in Collections:CIDMA - Artigos
CHAG - Artigos

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