Another cool math oriented picture

Submitted by Theoryful on Wed, 06/11/2008 at 4:08am.

In mathematics, E₈ is the name given to a family of closely related structures. In particular, it is the name of some exceptional simple Lie algebras as well as that of the associated simple Lie groups. It is also the name given to the corresponding root system, root lattice, and Weyl/Coxeter group, and to some finite simple Chevalley groups. E₈ was formulated between the years of 1888 and 1890 by Wilhelm Killing.

The designation E₈ comes from Wilhelm Killing and Élie Cartan's classification of the complex simple Lie algebras, which fall into four infinite families labeled A_n, B_n, C_n, D_n, and five exceptional cases labeled E₆, E₇, E₈, F₄, and G₂. The E₈ algebra is the largest and most complicated of these exceptional cases, and is often the last case of various theorems to be proved.

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Comments:

by Stavisky - 6 months ago
Essen-Antwerp Belgium

Member Since: Nov 2007
Member Points: 455

For me this is beautyfull math drawing,it's make me thinking about the fractals of Mandelbrot ( wich I think they are very beautyfull, but a little bit difficult to construct !) and in my opinion the upper one would be a beautyfull mandala ! Friendly greetings,

Herman

by normajeanyates - 6 months ago
london [often in calcutta india] England

Member Since: Jan 2008
Member Points: 2153

I wish I could draw a picture illustrating why π₅(S²)=Z/2Z [1]

Problem is i can prove it in various ways but i cant visualise it ... well it is the fundamental group of the 5-times-iterated loop space of the 2-sphere, so may be there is a real problem there visualising it, it's maybe not just me.

The contractibility of S^inf however would make a nice moving-picture - and everyone would understand it. Maybe I'll do it some day ...

[1] i write it that way rather than Z₂ because the latter is ambiguous -Z modulo 2, or 2-adic integers?

PS: Élie Cartan - one of my favourite mathematicians! Apart from his pure math work, he busted all this talk of 'general realativity=predetermined 4-dimensional universe" by putting newtonian mechanics in the same framework [only, newtonian mechanics has preferred-slices]. 'Popular science' books somehow never mention this - i mean one can understand the difficulty of bringing lie groups and lie algebras to the lay public, but this is unforgivable!

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