[GAP Forum] Re: Exceptional compact Lie algebras

[mim_ at op.pl]

Hi All,

Thank you very much for your answers and hints ! I have to study it and try in GAP.

Frankly speaking I am having doubts whether I understand when set of vectors form root system and how to decompose Lie algebra into root subspaces. In the real compact case these subspaces are 2-dimensional. 

For example for compact e6 there is decomposition into 6-dimensional Cartan algebra and 36 2-dimensional subspaces Vi. My hypothesis is that [Vi,Vj]=Vk for some k. Corresponding roots satisfy condition ri+rj=rk or ri-rj=rk. If you take two perpendicular vectors v,w from Vi, then [v,w] = ri and <v,w,ri> is isomorfic to su2.

Is this hypothesis true ?

Regards,
Marek Mitros

U¿ytkownik Frank Lübeck <frank.luebeck at math.rwth-aachen.de> napisa³:
>On Mon, Nov 05, 2007 at 12:41:59PM +0100, degraaf at science.unitn.it wrote:
>> Dear Marek Mitros,
>> 
>> >1. Do you have any ideas for building matrix representations of  
>> >compact e7, e8 in dimensions 56,248 respectively ?
>> 
>> Unfortunately I do not, but maybe somebody else does.
>
>Dear Forum,
>
>Just for the records: I have sent Marek generating matrices, including some
>which generate the subgroups he was looking for.
>
>Best regards,
>
> Frank
>
>-- 
>///  Dr. Frank Lübeck, Lehrstuhl D für Mathematik, Templergraben 64,  ///
>\\\\\\                    52062 Aachen, Germany                          \\\\\\
>///  E-mail: Frank.Luebeck at Math.RWTH-Aachen.De                        ///
>\\\\\\  WWW:    http://www.math.rwth-aachen.de/~Frank.Luebeck/           \\\\\\
>
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