``Möbius transformation for left-derivative quaternion holomorphic functions''

Citation:
Giardino, S.  2017.  ``Möbius transformation for left-derivative quaternion holomorphic functions''. Adv. Appl. Clifford Algebras (aceito para publica\c cão). 27(2):1161–1173.

Abstract:

Holomorphic quaternion functions only admit affine functions; thus, the Möbius transformation for these functions, which we call quaternionic holomorphic transformation (QHT), only comprises similarity transformations. We determine a general group X which has the group G of QHT as a particular case. Furthermore, we observe that the Möbius group and the Heisenberg group may be obtained by making X more symmetric. We provide matrix representations for the group X and for its algebra x. The Lie algebra is neither simple nor semi-simple, and so it is not classified among the classical Lie algebras. We prove that the group G comprises SU(2,C) rotations, dilations and translations. The only fixed point of the QHT is located at infinity, and the QHT does not admit a cross-ratio. Physical applications are addressed at the conclusion.

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