Question

Why do we start losing algebraic properties when dealing with hypercomplex numbers?

score 1.1k · Answer 1 · 2013-11-12 18:08:43

1.1k

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Why do we start losing algebraic properties when dealing with hypercomplex numbers?

Published on 12 Nov 2013 - 18:08

score 1.2k · Answer 2 · 2013-12-10 02:00:11

1.2k

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Quaternion Projective Space $\mathbb HP^n$ and Octonionic Projective Space $\mathbb OP^n$

Published on 10 Dec 2013 - 2:00

score 4.4k · Answer 3 · 2026-03-16 17:49:11

4.4k

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What specific algebraic properties are broken at each Cayley-Dickson stage beyond octonions?

Published on 16 Mar 2026 - 17:49

score 396 · Answer 4 · 2014-02-16 23:43:46

396

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What can you do with octonions?

Published on 16 Feb 2014 - 23:43

score 345 · Answer 5 · 2017-04-26 21:38:31

345

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Is there a slick proof for the identity that expresses the inner product of imaginary octonions in terms of the cross product?

Published on 26 Apr 2017 - 21:38

score 810 · Answer 6 · 2017-04-27 04:50:39

810

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Do the octonions form a field?

Published on 27 Apr 2017 - 4:50

score 122 · Answer 7 · 2017-07-05 00:26:32

122

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Is there a terminology that generalizes the "real part" and the "imaginary part"?

Published on 05 Jul 2017 - 0:26

score 428 · Answer 8 · 2017-08-11 01:33:58

428

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Why is SO(8) generated by left multiplications by octonions?

Published on 11 Aug 2017 - 1:33

score 394 · Answer 9 · 2017-08-17 10:23:05

394

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Characterizing lattices in $\mathbb{R}$, $\mathbb{C}$, $\mathbb{H}$ and $\mathbb{O}$ that are also rings

Published on 17 Aug 2017 - 10:23

score 293 · Answer 10 · 2017-09-16 23:09:53

293

Views

Is there a way to introduce quaternions and octonions in a similar way to how we are typically introduced to complex numbers?

Published on 16 Sep 2017 - 23:09

score 51 · Answer 11 · 2017-10-06 11:20:58

51

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Mirror symmetries of the Albert algebra

Published on 06 Oct 2017 - 11:20

score 95 · Answer 12 · 2017-10-08 08:42:30

95

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Is $ SL_2(\mathbb{O})$ a Lie group?

Published on 08 Oct 2017 - 8:42

score 44 · Answer 13 · 2026-03-25 16:06:39

44

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$\mathbb{S}^1$-action and octonionic multiplication can be associated

Published on 25 Mar 2026 - 16:06

score 203 · Answer 14 · 2017-10-29 09:08:39

203

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The geometric interpretation of quaternion and Octanion

Published on 29 Oct 2017 - 9:08

score 211 · Answer 15 · 2017-10-31 22:52:29

211

Views

Is octonion structure related to the fact that an 8-cube has an equal number of 2-faces and 3-cells?

Published on 31 Oct 2017 - 22:52

List Question

Why do we start losing algebraic properties when dealing with hypercomplex numbers?

Quaternion Projective Space $\mathbb HP^n$ and Octonionic Projective Space $\mathbb OP^n$

What specific algebraic properties are broken at each Cayley-Dickson stage beyond octonions?

What can you do with octonions?

Is there a slick proof for the identity that expresses the inner product of imaginary octonions in terms of the cross product?

Do the octonions form a field?

Is there a terminology that generalizes the "real part" and the "imaginary part"?

Why is SO(8) generated by left multiplications by octonions?

Characterizing lattices in $\mathbb{R}$, $\mathbb{C}$, $\mathbb{H}$ and $\mathbb{O}$ that are also rings

Is there a way to introduce quaternions and octonions in a similar way to how we are typically introduced to complex numbers?

Mirror symmetries of the Albert algebra

Is $ SL_2(\mathbb{O})$ a Lie group?

$\mathbb{S}^1$-action and octonionic multiplication can be associated

The geometric interpretation of quaternion and Octanion

Is octonion structure related to the fact that an 8-cube has an equal number of 2-faces and 3-cells?

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