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
[EMAIL PROTECTED] 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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