Timeline for Why/when classification of simple objects is "simple" ? E.g. (unknown) classification of simple Lie algebras in char =2,3...
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10 events
| when toggle format | what | by | license | comment | |
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| May 10, 2013 at 16:51 | comment | added | arsmath | There seems to be some dividing line where tightly constrained cases have a series/sporadic structure, and relaxing the constraint too much destroys this. For example, the classification of finite simple Moufang loops adds one additional series to the list of finite simple groups, while relaxing this slightly to Bol loops destroys any chances of classification. | |
| May 10, 2013 at 15:49 | answer | added | Dietrich Burde | timeline score: 2 | |
| May 10, 2013 at 13:32 | answer | added | Pasha Zusmanovich | timeline score: 5 | |
| Nov 25, 2012 at 10:45 | vote | accept | Alexander Chervov | ||
| Nov 21, 2012 at 17:34 | answer | added | Salvatore Siciliano | timeline score: 7 | |
| Nov 19, 2012 at 14:21 | comment | added | Nick Gill | @Qiaochu, as a general rule I would agree with you. However I think the Classification of Finite Simple Groups really does exhibit some kind of inherent series+sporadic behaviour. I wouldn't know how to formalise this - that might be a job for a logician (??) - but equally I don't think it can be explained away as a consequence of current mathematical culture. | |
| Nov 18, 2012 at 6:44 | comment | added | Alexander Chervov | @Qiaochu Yuan nevertheless we can say that "complexity" of such description is small - i.e. a code which will give for each natural "n" generators and relations of n-th simple Lie algebra (choose reasonable enumeration) will be quite short. (Kolmogorov's complexity is length of code to describe the object - as far as I understand). I am not sure it is equivalent to "series+sporadic", nevertheless it is measure of simplicity. | |
| Nov 18, 2012 at 1:22 | comment | added | Qiaochu Yuan | It is not clear to me that "series plus sporadic" is a property of a classification; it seems to me more like a property of a particular way of looking at a classification, which is dependent on the current knowledge, habits, tastes, etc. of specific groups of mathematicians. | |
| Nov 17, 2012 at 22:23 | comment | added | Will Sawin | Arguably, prime numbers do not form an infinite family in any sort of simple way. If you agree with that, then the classification of finite fields, finite simple groups, and some other things all fail to be simple. | |
| Nov 17, 2012 at 20:19 | history | asked | Alexander Chervov | CC BY-SA 3.0 |