Timeline for What are some examples of "chimeras" in mathematics?
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| May 28, 2012 at 8:55 | comment | added | Minhyong Kim | By the way, I think it's fine to think of a prime cyclic group as points of the additive group $\mathbb{G}_a$ in a prime finite field. They are the only possible simple groups of unipotent Lie type, the others being based on reductive groups. If we allow the `field with one element' you mentioned, this unifies all the infinite families. | |
| May 28, 2012 at 8:43 | comment | added | Minhyong Kim | whenever we tidy up a given list. I think I had initially thought of `chimeric' as conveying some sense of monstrosity, which I couldn't quite see in the list of finite simple groups. | |
| May 28, 2012 at 8:41 | comment | added | Minhyong Kim | I see what you mean. My own reaction that I still recall, upon first seeing the classification, was `It's really that simple?' My intuition, perhaps coming from the case-by-case classification of small finite groups done in a course, had expected an even more fragmented picture. Another analogy might be drawn to the case of primes numbers. In some sense, there is no classification of them. It seemed as though finite simple groups as well, because of their elementary nature, could have sprung up in a near random way everywhere, yet another unexpected type of very high order coming up (cont.) | |
| May 28, 2012 at 0:51 | comment | added | Terry Tao | It's not all that complicated, but it is "chimeric" in the sense that the different cases have a quite distinct character to them. In contrast, all the Lie algebras, whether classical or exceptional, come with reasonably similar-looking Dynkin diagrams, and that classification feels more "connected" in some way than that of the finite simple groups, which seems to have widely separated "connected components" in some sense. | |
| May 28, 2012 at 0:32 | comment | added | Minhyong Kim | I suppose there's some kind of a consensus that the proof is horrendous, but I don't quite see why you consider the result as complicated. Looks like a fairly compact list resembling the classification of simple Lie algebras, which many regard as the prototype of a nice classification theorem. | |
| May 27, 2012 at 23:56 | history | answered | Terry Tao | CC BY-SA 3.0 |