Timeline for What can be said about number-theoretic properties of the solid angle measures of polytopal cones in the weight lattice of sl(n)?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
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| Jan 3, 2012 at 14:58 | answer | added | Hugh Thomas | timeline score: 1 | |
| Dec 12, 2011 at 13:24 | comment | added | Bruce Westbury | @Alexander: I was thinking of taking the "scissors congruence" group over the rationals. Then the volume is a group homomorphism to the reals. Then I had in mind to reinterpret this in terms of $K$-theory and the Borel regulator. | |
| Dec 12, 2011 at 6:52 | history | edited | Theo Johnson-Freyd | CC BY-SA 3.0 |
Incorporated some comments
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| Dec 11, 2011 at 22:31 | comment | added | so-called friend Don | @Theo: I learned about it on math.stackexchange: Two proofs are at math.stackexchange.com/questions/79861/… | |
| Dec 11, 2011 at 22:27 | comment | added | Theo Johnson-Freyd | @Anonymous: Well, that seems to answer the first question. I'm sure that "If theta is a rational multiple of π, then 2cos(θ) is an algebraic integer" is well-known, but it is not well-known to me — can you point me to somewhere to read more? | |
| Dec 11, 2011 at 20:44 | comment | added | Alexander Woo | @Bruce: Could you explain the reason 'scissors congruence' might be related? Or is it just a hunch? | |
| Dec 11, 2011 at 20:32 | comment | added | Bruce Westbury | Have you looked into "scissors congruence"? | |
| Dec 11, 2011 at 20:19 | comment | added | so-called friend Don | It seems your pessimism is justified. If theta is a rational multiple of $\pi$, then $2\cos(\theta)$ is an algebraic integer. But if $\theta = \arctan(\sqrt{3}/5)$, then $2\cos(\theta) = 5/\sqrt{7}$. | |
| Dec 11, 2011 at 14:43 | comment | added | Ben Webster♦ | You correctly described the weight lattice; the root lattice is the intersection with that hyperplane rather than the projection. Unfortunately, that's the only part of your question I have much intelligent to say about. | |
| Dec 11, 2011 at 7:57 | history | asked | Theo Johnson-Freyd | CC BY-SA 3.0 |