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Dear Marco,

You asked:

am looking also for a list of the (low dimensional) Lie algebras over

finite fields, of the (low dimensional) restricted Lie algebras, and of

the (low dimensional) graded Lie algebras. Are there also such list

already available as gap input?

I do not have such lists; I do not even know whether such classifications

exist.

By the way, waiting for the lists, I enter some Lie algebras by hand,

giving the entries in the structure constant table, finding a strange

behavior of gap. Chapter 59.3, "Constructing Algebras by Structure

Constants" of the reference manual says: "For convenience, these entries

may also be rational numbers that are automatically replaced by the

corresponding elements in the appropriate prime field in finite

characteristic if necessary."

This means that if a structure constants table has been constructed

using the zero of a finite field, then entries enetered by SetEntrySCTable

will be converted to elements of that finite field.

for each p prime, we don't get this error any more, but we have to use a

different structure constant table for each prime. It would be more

convenient if it were possible to enter also the zero of the structure

constant table as rational, and to have it automatically replaced by the

corresponding elements in the appropriate prime field in finite

characteristic if necessary.

The function below does that for you.

With the best wishes,

Willem de Graaf

# Example of usage:

#

# gap> L:= SimpleLieAlgebra("G",2,Rationals);;

# gap> T:= StructureConstantsTable( Basis(L));;

# gap> MyLieAlgebraBySC( GF(3), T );

# <Lie algebra of dimension 14 over GF(3)>

MyLieAlgebraBySC:= function( F, T )

local dim, S, i, j;

dim:= Length( T )-2; S:= List( [1..dim], x -> [] ); Add( S, -1 ); Add( S, Zero(F) ); for i in [1..dim] do for j in [1..dim] do S[i][j]:= [ ShallowCopy( T[i][j][1] ), One(F)*T[i][j][2] ]; od; od; return LieAlgebraByStructureConstants( F, S ); end;

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