[GAP Forum] Lie Algebras over Complex field

[Marco Costantini]

Dear Manel Velasco and Gap forum

> I would like to know how to create a lie algeba structure over the
> complex numbres. Is it possile?

No, it is not possible, but it is possible to do something similar, which
could fit your needs.

The field of the complex numbers is not supported by Gap, hence it is not
possible to create structure over the complex numbers, but there are other
field implemented in Gap that could fit your needs: for instance
GaussianRationals (the smallest field including the square root of -1),
the other cyclotomic fields, and the algebraic extension of the Rarionals.
The relevant chapters in the documentation are the following.

http://www.gap-system.org/Manuals/doc/htm/ref/CHAP018.htm
http://www.gap-system.org/Manuals/doc/htm/ref/CHAP056.htm
http://www.gap-system.org/Manuals/doc/htm/ref/CHAP058.htm
http://www.gap-system.org/Manuals/doc/htm/ref/CHAP065.htm

Once that you have a field, then you can create a Lie algebra structure
over this field: see the documentation about Lie algebras at

http://www.gap-system.org/Manuals/doc/htm/ref/CHAP061.htm

This documentation should also be included in your Gap distribution.

Best regards,
Marco