Timeline for Which finite nonabelian groups have all their quaternionic representations of degree one?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| Jun 7, 2014 at 14:47 | vote | accept | Ken W. Smith | ||
| Jun 7, 2014 at 14:46 | vote | accept | Ken W. Smith | ||
| Jun 7, 2014 at 14:47 | |||||
| Jun 7, 2014 at 13:34 | history | edited | Ben Webster♦ | CC BY-SA 3.0 |
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| Jun 7, 2014 at 13:30 | comment | added | Ben Webster♦ | To any future readers: the comments above refer to my (wrong) previous answer. | |
| Jun 7, 2014 at 9:01 | history | edited | Ben Webster♦ | CC BY-SA 3.0 |
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| Jun 7, 2014 at 0:59 | comment | added | Ken W. Smith | Yes, I would have thought that every representation of the quaternion group of order 8 would be "linear" over the quaternions. If G = $\langle x, y : x^4=y^4=1, yxy^{-1}=x^3, x^2=y^2 \rangle$ then I have four reps over the rationals. In addition I guess I could map $x$ to $\pm i$, $y$ to $\pm j$ but are there more than four of these options possible? Do I lose control of my set of irreducibles? (I am so comfortable with the complex field that I have no good intuition with the strange noncommutative quaternion division ring!) | |
| Jun 6, 2014 at 21:48 | comment | added | Mark Wildon | Maybe I have misunderstood the question, but isn't every representation of the quaternion group of order 8 linear over the quaternions? | |
| Jun 6, 2014 at 20:52 | history | answered | Ben Webster♦ | CC BY-SA 3.0 |