Timeline for Cayley-Dickson form of a quaternion
Current License: CC BY-SA 4.0
13 events
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| Nov 3, 2022 at 11:08 | comment | added | Ben McKay | @Anixx: we need to think of the complex numbers as being the real span of $1,j$, not $1,i$, inside the quaternions. Then clearly with $ji=-k$ you can write every quaternion uniquely as $z+iw$ for complex numbers $z=x+jy$ and $w=u+jv$, for real numbers $x,y,u,v$. | |
| Nov 3, 2022 at 5:59 | comment | added | abx | Yes it is. See Bourbaki Algebra III, §2, no. 4: Cayley algebras. | |
| Nov 3, 2022 at 5:54 | history | edited | YCor | CC BY-SA 4.0 |
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| Nov 3, 2022 at 5:52 | comment | added | Anixx | I do not know where you got this from, but this is not Cayley-Dickson construction. Instead, the form you give in the question is a representation of bicomplex numbers, which are not quaternions. | |
| May 5, 2011 at 9:33 | answer | added | Tom De Medts | timeline score: 6 | |
| Apr 20, 2011 at 21:34 | answer | added | Ted Shaneyfelt | timeline score: 0 | |
| Feb 3, 2010 at 18:30 | comment | added | José Figueroa-O'Farrill | Moreover, I would say that the Cayley-Dickson process would write the quaternion as a pair $(x,y)$ of complex numbers and not in the way that it is written in the question. | |
| Feb 3, 2010 at 18:28 | comment | added | José Figueroa-O'Farrill | I believe that this might be engineering nomenclature, who also use the term "symplectic" in the same sense as in the question. I have never come across this usage of symplectic (although I can see why it is used) or "simplex" and "perplex" parts in the mathematics or mathematical physics literature. | |
| Feb 3, 2010 at 17:38 | comment | added | Charles Siegel | I'm with Johannes, I've never seen a simplex-part or perplex-part mentioned anywhere...what references used those terms? | |
| Feb 3, 2010 at 17:15 | comment | added | Johannes Hahn | Personally I've never read or heard the terms "simplex part" and "perplex part". | |
| Feb 3, 2010 at 16:54 | history | edited | zipuni | CC BY-SA 2.5 |
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| Feb 3, 2010 at 16:49 | history | edited | darij grinberg |
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| Feb 3, 2010 at 16:47 | history | asked | zipuni | CC BY-SA 2.5 |