Timeline for In the quaternions, "any imaginary unit may be called i"
Current License: CC BY-SA 2.5
13 events
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| Jun 15, 2020 at 7:27 | history | edited | CommunityBot |
Commonmark migration
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| Feb 1, 2011 at 18:28 | comment | added | Qfwfq | @Emerton: thanks for the explanation. | |
| Feb 1, 2011 at 3:09 | vote | accept | Daniel Briggs | ||
| Jan 31, 2011 at 17:10 | comment | added | Daniel Briggs | @Mark Sapir: No, I guess that does about wrap it up, without a need to change to the context of category theory. I will accept Emerton's answer later today. | |
| Jan 31, 2011 at 14:23 | comment | added | Emerton | Dear unknowngoogle, it's not the case case that $SO(3) \times SO(3)$ is isomorphic to $SO(4)$; there is a central isogeny from the latter to the former, with kernel of order 2. (One has a succession of degree 2 central isogenies $SU(2) \times SU(2) \to SO(4) \to SO(3) \times SO(3)$. The latter isogeny induces the isomorphism $PSO(4) \to PSO(3) \times PSO(3) = SO(3) \times SO(3)$ which the OP is referring to.) | |
| Jan 31, 2011 at 12:52 | comment | added | Qfwfq | Also, why are you using $PSO_3$, $PSO_4$ and not just $SO_3$, $SO_4$ ? | |
| Jan 31, 2011 at 3:40 | answer | added | Emerton | timeline score: 20 | |
| Jan 30, 2011 at 23:39 | comment | added | Qfwfq | It's a standard (easy) fact that the quaternions that square to −1 form a 2-sphere in the purely imaginary quaternions. And automorphisms act transitively on that sphere... | |
| Jan 30, 2011 at 23:39 | comment | added | user6976 | Is that true that the 2 lines of Mariano's comments are equivalent to the 40+ lines of the question? Or did I miss something important? | |
| Jan 30, 2011 at 22:34 | comment | added | Mariano Suárez-Álvarez | Do you have an use for your "vision"? If what you want is simply to know whether "all units are created equal", then you can simply prove that the automorphism group of the algebra acts transitively on the set of elements which square to $-1$. | |
| Jan 30, 2011 at 21:44 | history | edited | Daniel Briggs | CC BY-SA 2.5 |
added 365 characters in body
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| Jan 30, 2011 at 21:06 | history | edited | Daniel Briggs | CC BY-SA 2.5 |
changed category-theoretic context at end; added 13 characters in body
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| Jan 30, 2011 at 20:56 | history | asked | Daniel Briggs | CC BY-SA 2.5 |