How to define the classical Lie algebras using the GAP package?

Question

How to define using the GAP package, with the Lie algebra package included, some classical Lie algebras like sl(n,C), so(n,R), su(n) etc. without using commands referring to the type A_n?

• Possibly one has first to define the corresponding associative algebras.

• Or one has to define first the classical groups SL(n,C), SO(R,n), SU(n) and then apply a command which gives the Lie algebra of a Lie group? Which command?

Answer 1

Use the user-contributed Lie algebra package by Willem de Graaf and Thomas Breuer for GAP, see here.