Möbius gyrogroups: a Clifford algebra approach.
This article continues the investigations of the first author [in Adv. Appl. Clifford Algebr. 19, No. 2, 303-323 (2009; Zbl 1197.20056)] restricting the interest to the finite dimensional case and giving more details. In particular they use their results to study the sections of Möbius fiber bundles inherited by the Möbius projectors. For more details we refer the reader to the authors' summary: ``Using the Clifford algebra formalism we study the Möbius gyrogroup of the ball of radius \(t\) of the paravector space \(\mathbb R\oplus V\), 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.''
finite-dimensional real Clifford algebras
scientific article; zbMATH DE number 5888491
scientific article