[GAP Forum] Re: Exceptional compact Lie algebras

[Shaun Van Ault]

Dear Marek Mitros,
   You may also want to look into the LiE system

http://wwwmathlabo.univ-poitiers.fr/~maavl/LiE/

   This system offers many built-in Lie functions that seem to perform 
faster than their GAP counterparts.  On the downside, the scripting 
language associated with LiE is not very powerful, so you may need to 
write programs in another language accessing the LiE functions only when 
necessary.  There is a GAP-LiE interface, called "liegap", but for the 
life of me, I cannot remember how to obtain it!  I do have a copy of the 
  binaries for "liegap", though, if you are interested.

Best,
-Shaun Ault



degraaf at science.unitn.it wrote:
> Dear Marek Mitros,
> 
> You asked some questions about constructing compact forms of exceptional
> Lie algebras in GAP. I may have some partial answers to your questions.
> 
>> 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.
> 
>> 2. The root system in GAP is different to the one presented on 
>> wikipedia for F4, E6,E7,E8. Is there way to take wikipedia roots and 
>> build lie algebra from it ?
> 
> Not directly. However, the simple Lie algebras in GAP come with a root 
> system,
> that have a Cartan matrix and a system of simple roots. One can use this
> data to identify the GAP root system with any other preferred one.
> 
>> 3. When I tried to do Derivations from 54 dimensional algebra C*h3O 
>> there is out-of-memory error which close the GAP session. Any 
>> workaround ?
> 
> The algorithm for computing derivations solves a rather large amount of 
> linear
> equations. This may indeed lead to memory problems. But I don't know of any
> other algorithm to compute derivations.
> 
> Best wishes,
> 
> Willem de Graaf
> 
> 
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