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Möbius gyrogroups: a Clifford algebra approach
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Orientador(es)
Resumo(s)
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.
Descrição
Palavras-chave
Möbius gyrogroups Möbius projectors Quotient Möbius gyrogroups Möbius fiber bundles
Contexto Educativo
Citação
Ferreira M., and Ren G., Möbius gyrogroups: A Clifford algebra approach, J. Algebra 328(1) (2011), 230-253
Editora
Elsevier