@article {Giardino:2015dza,
	title = {{\textquoteleft}{\textquoteleft}M{\"o}bius transformation for left-derivative quaternion holomorphic functions{\textquoteright}{\textquoteright}},
	journal = {Adv. Appl. Clifford Algebras (aceito para publica\c c{\~a}o)},
	volume = {27},
	year = {2017},
	pages = {1161{\textendash}1173},
	abstract = {<p>Holomorphic quaternion functions only admit affine functions; thus, the M{\"o}bius 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 M{\"o}bius 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.</p>
},
	doi = {10.1007/s00006-016-0673-y},
	url = {https://doi.org/10.1007/s00006-016-0673-y},
	author = {S. Giardino}
}
