<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">S. Giardino</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">``Möbius transformation for left-derivative quaternion holomorphic functions''</style></title><secondary-title><style face="normal" font="default" size="100%">Adv. Appl. Clifford Algebras (aceito para publica\c cão)</style></secondary-title></titles><dates><year><style  face="normal" font="default" size="100%">2017</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://doi.org/10.1007/s00006-016-0673-y</style></url></web-urls></urls><volume><style face="normal" font="default" size="100%">27</style></volume><pages><style face="normal" font="default" size="100%">1161–1173</style></pages><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;p&gt;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.&lt;/p&gt;
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