Mobius gyrogroups: A Clifford algebra approach

Using the Clifford algebra formalism we study the Mobius gyrogroup of the ball of radius t of the paravector space R circle plus V, where V is a finite-dimensional real vector space. We characterize all the gyro-subgroups of the Mobius 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 Mobius gyrogroups. With the algebraic structure of the factorizations we study the sections of Mobius fiber bundles inherited by the Mobius projectors. (C) 2010 Elsevier Inc. All rights reserved.