IsSemiSimple
check if a LAVF is semi-simple.
Calling Sequence
Parameters
Description
Examples
Compatibility
IsSemiSimple( obj)
obj
-
a LAVF object that is a Lie algebra i.e.IsLieAlgebra(obj) returns true, see IsLieAlgebra.
Let L be a LAVF object which is a Lie algebra. Then IsSemiSimple method returns true if and only if L is semisimple i.e. the solvable radical of L is trivial. False otherwise.
This method is associated with the LAVF object. For more detail, see Overview of the LAVF object.
withLieAlgebrasOfVectorFields:
Typesetting:-Settingsuserep=true:
Typesetting:-Suppressξx,y,ηx,y:
V≔VectorFieldξx,yDx+ηx,yDy,space=x,y
V≔ξⅆⅆx+ηⅆⅆy
E2≔LHPDEdiffξx,y,y,y=0,diffηx,y,x=−diffξx,y,y,diffηx,y,y=0,diffξx,y,x=0,indep=x,y,dep=ξ,η
E2≔ξy,y=0,ηx=−ξy,ηy=0,ξx=0,indep=x,y,dep=ξ,η
Construct a LAVF for the Euclidean Lie algebra E(2).
L≔LAVFV,E2
L≔ξⅆⅆx+ηⅆⅆy&whereξy,y=0,ξx=0,ηx=−ξy,ηy=0
IsLieAlgebraL
true
IsSemiSimpleL
false
The IsSemiSimple command was introduced in Maple 2020.
For more information on Maple 2020 changes, see Updates in Maple 2020.
See Also
LieAlgebrasOfVectorFields (Package overview)
LAVF (Object overview)
LieAlgebrasOfVectorFields[VectorField]
LieAlgebrasOfVectorFields[LHPDE]
LieAlgebrasOfVectorFields[LAVF]
IsLieAlgebra
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