annihilator(FGLieSubAlgebra) -- make the annihilator Lie subalgebra

Synopsis

• Function: annihilator

• Usage:

  A=annihilator(S)

• Inputs:
  • S, an instance of the type FGLieSubAlgebra,
• Optional inputs:
  • Strategy => ..., default value null,
• Outputs:
  • A, an instance of the type LieSubAlgebra, the Lie subalgebra of L=S#lieAlgebra consisting of the set $A$ of elements $x$ in $L$ such that $x y=0$ for all $y$ in $S$.

Description

i1 : L = lieAlgebra{a,b,c}/{a a c+b a c,c c a}

o1 = L

o1 : LieAlgebra

i2 : S=lieSubAlgebra({a c})

o2 = S

o2 : FGLieSubAlgebra

i3 : A=annihilator(S)

o3 = A

o3 : LieSubAlgebra

i4 : dims(1,4,A)

o4 = {2, 2, 2, 3}

o4 : List

i5 : basis(3,A)

o5 = {(b c a) + (b c b) - (c b a), (c c b)}

o5 : List

See also

• quotient(LieIdeal,FGLieSubAlgebra) -- make the quotient of a Lie ideal by a finitely generated Lie subalgebra