[GAP Forum] Re: Exceptional compact Lie algebras

[degraaf at science.unitn.it]

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