Editing Split-quaternion (section)

== Historical notes ==

The coquaternions were initially introduced (under that name)<ref>[[James Cockle]] (1849), [https://www.biodiversitylibrary.org/item/20114#page/448/mode/1up On Systems of Algebra involving more than one Imaginary], ''[[Philosophical Magazine]]'' (series 3) 35: 434,5, link from [[Biodiversity Heritage Library]]</ref> in 1849 by [[James Cockle]] in the London&ndash;Edinburgh&ndash;Dublin [[Philosophical Magazine]]. The introductory papers by Cockle were recalled in the 1904 ''Bibliography''<ref>A. Macfarlane (1904) [http://dlxs2.library.cornell.edu/cgi/t/text/text-idx?c=math;cc=math;view=toc;subview=short;idno=03030001 Bibliography of Quaternions and Allied Systems of Mathematics], from [[Cornell University]] ''Historical Math Monographs'', entries for James Cockle, pp.&nbsp;17–18</ref> of the [[Quaternion Society]].

[[Alexander Macfarlane]] called the structure of split-quaternion vectors an ''exspherical system'' when he was speaking at the [[International Congress of Mathematicians]] in Paris in 1900.<ref>A. Macfarlane (1900) [http://www.mathunion.org/ICM/ICM1900/Main/icm1900.0305.0312.ocr.pdf Application of space analysis to curvilinear coordinates] {{Webarchive|url=https://web.archive.org/web/20140810042126/http://www.mathunion.org/ICM/ICM1900/Main/icm1900.0305.0312.ocr.pdf |date=2014-08-10 }}, ''Proceedings of the ''[[International Congress of Mathematicians]], Paris, page 306, from [[International Mathematical Union]]</ref> Macfarlane considered the "hyperboloidal counterpart to spherical analysis" in a 1910 article "Unification and Development of the Principles of the Algebra of Space" in the ''Bulletin'' of the [[Quaternion Society]].<ref>A. Macfarlane (1910) [https://archive.org/details/proceedingsfifth00hobs/page/266/mode/2up "Unification and Development of the Principles of the Algebra of Space"] via Internet Archive.</ref>

[[Hans Beck (mathematician)|Hans Beck]] compared split-quaternion transformations to the circle-permuting property of [[Möbius transformation]]s in 1910.<ref>[[Hans Beck (mathematician)|Hans Beck]] (1910) [http://www.ams.org/journals/tran/1910-011-04/S0002-9947-1910-1500872-0/S0002-9947-1910-1500872-0.pdf Ein Seitenstück zur Mobius'schen Geometrie der Kreisverwandschaften], [[Transactions of the American Mathematical Society]] 11</ref> The split-quaternion structure has also been mentioned briefly in the ''[[Annals of Mathematics]]''.<ref>[[A. A. Albert]] (1942), "Quadratic Forms permitting Composition", ''[[Annals of Mathematics]]'' 43:161 to 77</ref><ref>[[Valentine Bargmann]] (1947), [https://www.jstor.org/discover/10.2307/1969129 "Irreducible unitary representations of the Lorentz Group"], ''[[Annals of Mathematics]]'' 48: 568&ndash;640</ref>