Timeline for Looking for root system in finite simple groups
Current License: CC BY-SA 3.0
7 events
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| Jan 1, 2019 at 16:49 | comment | added | LSpice | You mention "We can use terms from Lie groups in finite groups of Lie type." The reason for this is that many such terms have been generalised from (linear) Lie groups to the setting of linear algebraic groups over arbitrary fields, and that, at least according to most definitions (but see @JimHumphreys's post discussing the fact that there is no one correct such), a finite group of Lie type is the group of rational points of a linear algebraic group over a finite field. | |
| Aug 17, 2017 at 8:54 | history | edited | user21230 | CC BY-SA 3.0 |
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| Aug 16, 2017 at 15:32 | comment | added | Jim Humphreys | I just meant that in your question you use $q$ for an arbitrary finite group without specifying it. Of course, groups of Lie type do have a natural characteristic, but others such as alternating groups get tricky. (Also, the notion of "maximal torus" doesn't immediately make sense for an arbitrary finite group.) | |
| Aug 16, 2017 at 13:35 | comment | added | user21230 | The groups of "Lie type" have natural characteristic. Can you explain your last sentence, what do you mean by "try to avoid it at first" ? It is kind of paradox you use. I encountered word "maximal torus" used for finite groups of Lie type. This means that people try to use notions from compact Lie groups to finite ones. | |
| Aug 16, 2017 at 13:01 | comment | added | Jim Humphreys | The question is natural but difficult, and versions of it have (I believe) been raised at times in connection with the classification of finite simple groups. But a big problem at the outset is to assign a "natural" characteristic $p$ (or a power $q$ of it) to an arbitrary simple group. You recognize this problem but try to avoid it at first even though it's unavoidable. | |
| Aug 16, 2017 at 9:28 | history | edited | user21230 | CC BY-SA 3.0 |
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| Aug 16, 2017 at 9:23 | history | asked | user21230 | CC BY-SA 3.0 |