Timeline for What would you want on a Lie theory cheat poster?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Feb 5, 2019 at 12:13 | history | edited | Glorfindel | CC BY-SA 4.0 |
broken image fixed (click 'rendered output' to see the difference); for more info, see https://gist.github.com/Glorfindel83/9d954d34385d2ac2597bbe864466259f
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| May 1, 2011 at 11:13 | comment | added | André Henriques | I'd like someone (Bruce?) to make a better picture of the Vogel plane. Is it really A_1^3 and not A_1^2? Isn't there an extra A_1 in the line through E_8? And... of course, E_8 is not visible! | |
| Apr 28, 2011 at 16:36 | comment | added | Noah Snyder | Hrm, good question... The description of the Vogel plane that I'm most familiar with seems like it should identify sl(2) and so(3) at the same point. My guess is that what Bruce has written down there is actually a ramified cover of that P^2 where he's also keeping track of the choice of defining representation. As such so(3) might better be labelled SO(3). But I'm not totally sure. | |
| Apr 28, 2011 at 6:25 | comment | added | S. Carnahan♦ | It looks like some exceptional low-rank isomorphisms aren't identified. Am I missing something? | |
| Apr 26, 2011 at 20:32 | comment | added | Noah Snyder | So there's two issues here: one is how meaningful the points in the plane are, the other is how meaningful the lines are. Dylan's paper actually gives (a very small amount of) evidence in support of the conjecture that every point in the plane determines at most one Lie algebra object. It also gives (a very small amount of) evidence against the idea that every point actually gives a Lie algebra object. What it conclusively shows is that there's no line going through F4 or E6 consisting of Lie algebras objects whose representation theory looks like F4 or E6. | |
| Apr 26, 2011 at 20:11 | comment | added | André Henriques | From Bruce's website: "The idea is that this should be thought of as a two-parameter family of Lie algebras which contains every simple Lie algebra. The three vertical lines are the three families of classical simple Lie algebras. The other two lines are the last two rows of the Freudenthal magic square." Is that really true? What about this paper of Dylan Thurston math.columbia.edu/~dpt/writing/F4E6.ps that claims to have evidence against that conjecture? | |
| Apr 26, 2011 at 19:04 | comment | added | Bruce Westbury | I'm flattered! Please don't take this picture too seriously. | |
| Apr 26, 2011 at 18:41 | history | answered | Noah Snyder | CC BY-SA 3.0 |