Question

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

score 1.1k · Answer 1 · 2026-04-10 04:39:18

1.1k

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

Published on 10 Apr 2026 - 4:39

score 1.2k · Answer 2 · 2026-04-15 08:54:16

1.2k

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

Published on 15 Apr 2026 - 8:54

score 4.4k · Answer 3 · 2026-04-27 11:56:43

4.4k

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

Published on 27 Apr 2026 - 11:56

score 397 · Answer 4 · 2026-03-26 01:01:45

397

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What can you do with octonions?

Published on 26 Mar 2026 - 1:01

score 348 · Answer 5 · 2026-04-11 04:33:29

348

Views

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

Published on 11 Apr 2026 - 4:33

score 811 · Answer 6 · 2026-03-25 19:01:06

811

Views

Do the octonions form a field?

Published on 25 Mar 2026 - 19:01

score 125 · Answer 7 · 2026-04-13 02:32:22

125

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

Published on 13 Apr 2026 - 2:32

score 429 · Answer 8 · 2026-03-25 19:03:15

429

Views

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

Published on 25 Mar 2026 - 19:03

score 397 · Answer 9 · 2026-04-11 03:23:40

397

Views

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

Published on 11 Apr 2026 - 3:23

score 296 · Answer 10 · 2026-04-14 21:52:27

296

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 14 Apr 2026 - 21:52

score 53 · Answer 11 · 2026-05-10 17:20:28

53

Views

Mirror symmetries of the Albert algebra

Published on 10 May 2026 - 17:20

score 98 · Answer 12 · 2026-04-10 11:32:24

98

Views

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

Published on 10 Apr 2026 - 11:32

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

44

Views

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

Published on 25 Mar 2026 - 16:06

score 205 · Answer 14 · 2026-04-10 20:41:30

205

Views

The geometric interpretation of quaternion and Octanion

Published on 10 Apr 2026 - 20:41

score 216 · Answer 15 · 2026-04-17 00:02:06

216

Views

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

Published on 17 Apr 2026 - 0:02

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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