Hi,

I tried to find the set of real parameters a1, a2, a3, a4 and u1, u2, u3 which make a subalgebra L an ideal of a finite real Lie algebra LieAlg. Unfortunately, the "Query" command with the "Ideal" argument returns an error message that I can't get around. What should I change in this command?

restart: 
with(DifferentialGeometry):
with(LieAlgebras):
#
DGsetup([x1,x2,x3],R3):
#
Lie_Generators := [D_x1*x1+D_x2*x2+D_x3*x3, D_x3*k^2*x1+D_x1*x3, -D_x1*x2+D_x2*x1, D_x3*k^2*x2+D_x2*x3, D_x1, D_x2, D_x3]:
#
LieAlg:=LieAlgebraData(Lie_Generators):
#
DGsetup(LieAlg):
#
L:= evalDG([e3+u2*e5-u1*e6,e2-u3*e5-k^2*u1*e7,e4-u3*e6-k^2*u2*e7,e1-u1*e5-u2*e6-u3*e7]);
Sub_Alg_L:=LieAlgebraData(L);
#
TrueFalse,Equations,Solutions,IdealList:=Query(L,{u1,u2,u3},"Ideal");
#
TrueFalse,Equations,Solutions,IdealList:=Query([DGzip([a1,a2,a3,a4], L, "plus")],{a1,a2,a3,a4,u1,u2,u3},"Ideal");

Thanks for your help.

Jaqr

Hi,

The evalDG command included in the LieAlgebras via the DifferentialGeometry package allows summations such as evalDG(e1+e2) where e1 and e2 are two generators of a given Lie algebra.

Now, let L be a list of such summations, e.g.,

L= [e1+a*e3,2*e2+b*e4,e1+3*e5]

where a and b are symbols for variable names in the real domain.
Then, while the code

evalDG(add(eval(cat(e,i)),i=1..n));

works fine (n be a given integer), the code

evalDG(add(eval(L[i]),i=1..n));

does not, and an error message results due to an "invalid subscript selector".

What is the right code to realize this summation?

Thanks.

Jaqr

Hi!

Does it exist a command in the LieAlgebras package to find the list of normal subalgbras of a given finite dimensional Lie algebra?

Thank.

Hi!

I used the command "Decompose" for the following trivial 2 dimensional abelian Lie algebra:

This command returns an error:

Alg:=[D_x,D_y]:
Alg_L:=LieAlgebraData(Alg):
DGsetup(Alg_L):
Decompose();

Error, (in print/_DG) final value in for loop must be numeric or character

Why this issue?

Thanks

Hi!

What could be a fast procedure to cancel uncommon factors of terms in such following sets (list) and simplify:

Starting with:

{a*x,b*x, c*(x+y)}

(where a, b and c are numbers or in set of specified variables as well as x and y), I would like as a result:

{x,x+y}

Many thanks.

Jaqr