Ciao Mimmo,
You asked about restricted enveloping algebras. In fact, some time
ago I have written a small package containing a function for creating
these algebras. It is called `penvelope', and can be found on my
homepage, www.math.uu.nl/people/graaf/penv.html.
An example:
gap> RequirePackage("penvelope"); PEnvelope! true gap> L:= SimpleLieAlgebra("A",2,GF(3) ); <Lie algebra of dimension 8 over GF(3)> gap> u:= PEnvelopingAlgebra( L ); PEnvAlgebra( <Lie algebra of dimension 8 over GF(3)> ) gap> g:= GeneratorsOfAlgebra(u); [ (Z(3)^0)*1, (Z(3)^0)*x1, (Z(3)^0)*x2, (Z(3)^0)*x3, (Z(3)^0)*x4, (Z(3)^0)*x5, (Z(3)^0)*x6, (Z(3)^0)*x7, (Z(3)^0)*x8 ] gap> g[3]^3; <zero> gap> g[8]^3; (Z(3)^0)*x7 gap> g[8]^4*g[5]^2*g[2]; (Z(3)^0)*x1*x4^2+(Z(3))*x1*x4^2*x7+(Z(3)^0)*x1*x4^2*x7^2+(Z(3))*x4+(Z(3)^0)*x 4*x7^2
If you have questions about it, please ask.
All the best,
Willem
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