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

Synopsis

• Function: quotient

• Usage:

  T=quotient(I,S)

• Inputs:
  • I, an instance of the type LieIdeal
  • S, an instance of the type FGLieSubAlgebra
• Optional inputs:
  • BasisElementLimit => ..., default value infinity,
  • DegreeLimit => ..., default value {},
  • MinimalGenerators => ..., default value true,
  • PairLimit => ..., default value infinity,
  • Strategy => ..., default value null,
• Outputs:
  • T, an instance of the type LieSubAlgebra, the Lie elements that multiply all of $S$ into $I$

Description

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

o1 = L

o1 : LieAlgebra

i2 : I=lieIdeal{a}

o2 = I

o2 : FGLieIdeal

i3 : S=lieSubAlgebra{b,c}

o3 = S

o3 : FGLieSubAlgebra

i4 : K=quotient(I,S)

o4 = K

o4 : LieSubAlgebra

i5 : basis(2,K)

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

o5 : List

See also

• annihilator(FGLieSubAlgebra) -- make the annihilator Lie subalgebra
• inverse(LieAlgebraMap,LieSubSpace) -- make the inverse image of a Lie subspace under a Lie algebra map