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Dear Ilya Yanok,

You asked:

How can I get all subalgebras (up to isomorphism) of given Lie algebra?

I don't know of any algorithm for that. It seems to be a very difficult

task. There certainly is no function in GAP that will do that.

How can I check if Lie algebra a is isomophic to another Lie algebra b?

This is rather difficult as well. If both Lie algebras are semisimple

then the solution is easy: just compute the root system of each

Lie algebra. In general it can be done by a Groebner basis computation.

This will work for small dimensional Lie algebras (it depends a bit on

the structure of the Lie algebras to which dimension one can get).

I have written some functions for that which are part of a small

package which you can download from

http://www.math.uu.nl/people/graaf/singular.html

This contains an interface to the system Singular, which does the

Groebner basis computations. In order to use this you have to install

Singular, which you can get from

http://www.singular.uni-kl.de/

Furthermore, the operating system of your computer must be Unix,

otherwise the interface will not work.

All the best,

Willem de Graaf

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