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E8 Structure Decoded

Posted by Hemos on from the get-it-down-on-paper dept.

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)."

13 of 127 comments (clear)

  1. Pronounce it "Lee-eh" by G3ckoG33k · · Score: 3, Informative

    Pronounce it "Lee-eh"; At least that is how I would do it as a Scandinavian.

    1. Re:Pronounce it "Lee-eh" by Anonymous Coward · · Score: 4, Informative

      As a Norwegian, I would pronounce it "Lee". It's a bit strange I agree, but that's how that name is usually pronounced.

    2. Re:Pronounce it "Lee-eh" by G3ckoG33k · · Score: 4, Informative

      Thanks!

      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...

  2. mandatory Wikipedia link by cpct0 · · Score: 4, Informative

    http://en.wikipedia.org/wiki/E8_(mathematics)

    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.

  3. Re:No practical applications? by necro81 · · Score: 4, Informative

    But of course it has practical applications: it applies to string theory!

  4. Not a Lie Group. by WK2 · · Score: 3, Informative

    E8 is not a Lie Group. E8 is the biggest Lie Group. Here are a few links for more accurate info:

    http://news.bbc.co.uk/2/hi/science/nature/6466129. stm
    http://en.wikipedia.org/wiki/E8_(mathematics)

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    1. Re:Not a Lie Group. by Anonymous Coward · · Score: 1, Informative

      Actually, it is not the biggest, it is "just" the most complex.

      It does not get even into top ten as there are infinite number of bigger Lie groups :-)

  5. Representation Theory by l2718 · · Score: 5, Informative

    Apologies -- this post uses a lot of technical jargon. However, the article is so badly written that I decided to post some remarks. And yes, I am a professional mathematician.

    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.

    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.

    1. Re:Representation Theory by nanosquid · · Score: 2, Informative

      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.

      Well, maybe that's surprising to some mathematicians, but this sort of thing is nearly half a century old.

  6. See the symmetries of the standard model by sweetser · · Score: 4, Informative

    Hello:

    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/ 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/quan tum/standard_model/standard_model.html

    doug

    --
    Working on new views of old physics at http://VisualPhysics.org
  7. Re:iPod by Short+Circuit · · Score: 2, Informative

    Nope. Actually, it's 129.453827 kbps. (Is there anything Google can't do?)

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  8. Re:Sage the "super" computer by Anonymous Coward · · Score: 1, Informative

    It is just our luck that the the server room is undergoing major renovations this week...

    See a mirror, e.g. http://sage.scipy.org/sage/

    FYI, sage is fully (GPL/GPL-compatible) open source.

  9. Re:What are the generators? by leuffi · · Score: 2, Informative

    E8 is not a finite group so it cannot be embedded in a finite symmetric group.