E8 Structure Decoded 127
arobic writes "A group of mathematicians from US and Europe succeeded in mapping the E8 structure, an example of a Lie group. These were developed by the well-known mathematician Sophus Lie (pronounce Lee) in the last century and are used for many applications, mainly in theoretical physics. This is an important breakthrough as it could help physicists working on Grand Unified Theories (aka GUTs)."
Pronounce it "Lee-eh" (Score:4, Informative)
mandatory Wikipedia link (Score:5, Informative)
Seriously, these articles, as most in Math category, are totally undecipherable to most normal users. TG there is a Wikipedia somewhere, sometimes they are closer to layman.
Re:No practical applications? (Score:5, Informative)
Not a Lie Group. (Score:3, Informative)
http://news.bbc.co.uk/2/hi/science/nature/6466129
http://en.wikipedia.org/wiki/E8_(mathematics) [wikipedia.org]
Representation Theory (Score:5, Informative)
First, what they mapped was not the "structure" of the Lie group E_8 -- the structure of the group has been known for a long time. What they mapped is what are called the "representations" of the group E_8, which is part of Vogan's program to understand the "unitary dual" (=list of representations) for all (reductive) Lie groups.
Second, this has no relevance to grand unified theories. Even though a (compact) form of E_8 can be the gauge group of a GUT, the relevant representations are finite-dimensional and have been classified by Weyl decades ago [wikipedia.org].
Finally, this is an important result. It is relevant to number theory, and to abstract mathematics in general. The fact that a (finite) computer calculation can help determining an infinite list of representation is very nice.
Re:Pronounce it "Lee-eh" (Score:4, Informative)
Re:Pronounce it "Lee-eh" (Score:5, Informative)
I had to check it with a Norwegian colleague, who confirmed you pronunciation.
(I had thought it meant 'scythe' (Sw. 'lie', No. 'ljå' [pronouced 'yaw'!]), but actually it was 'slope' (Sw. lid; with a pronouned 'd' in the high form, but silent in dialectal forms).
So, all those years calling the Tryggve Lie a scythe was in in vain...
See the symmetries of the standard model (Score:4, Informative)
The standard model has the symmetries U(1)xSU(2)xSU(3). The one in the middle, SU(2), is a unit quaternion, where a quaternion is like a real or complex number, but has four parts. I have developed the software to visualize quaternions at http://quaternions.sf.net/ [sf.net] using one number for time, three for space. SU(2) can be represented by the quaternion function exp(q-q*). Feed a thousand random quaternions into exp(q-q*), and get POVRay to make a nice animation. Do the same for q/|q| exp(q-q*), and you have a visual representation of the electroweak symmetry. Smash two of these together, and you get the symmetry of the standard model.
Visually, there is a clear message: if you want to smoothly represent all possible events in spacetime as quaternions, the group description must be U(1)xSU(2)xSU(3). You won't read that in a journal because it has to be done with animations.
http://www.theworld.com/~sweetser/quaternions/qua
doug
Re:Not a Lie Group. (Score:1, Informative)
It does not get even into top ten as there are infinite number of bigger Lie groups
Re:Representation Theory (Score:2, Informative)
Well, maybe that's surprising to some mathematicians, but this sort of thing is nearly half a century old.
Re:iPod (Score:2, Informative)
Re:Sage the "super" computer (Score:1, Informative)
See a mirror, e.g. http://sage.scipy.org/sage/ [scipy.org]
FYI, sage is fully (GPL/GPL-compatible) open source.
Re:What are the generators? (Score:2, Informative)