Möbius gyrogroups: a Clifford algebra approach

• Main Author: Ferreira, Milton
• Publication Date: 2011
• Other Authors: Ren, G.
• Format: Article
• Language: eng
• Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
• Download full: http://hdl.handle.net/10400.8/3817
• topic: Möbius gyrogroups; Möbius projectors; Quotient Möbius gyrogroups; Möbius fiber bundles

Using the Clifford algebra formalism we study the Möbius gyrogroup of the ball of radius t of the paravector space, where V is a finite-dimensional real vector space. We characterize all the gyro-subgroups of the Möbius gyrogroup and we construct left and right factorizations with respect to an arbitrary gyro-subgroup for the paravector ball. The geometric and algebraic properties of the equivalence classes are investigated. We show that the equivalence classes locate in a k-dimensional sphere, where k is the dimension of the gyro-subgroup, and the resulting quotient spaces are again Möbius gyrogroups. With the algebraic structure of the factorizations, we study the sections of Möbius fiber bundles inherited by the Möbius projectors.