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GradedLieAlgebras :: LieAlgebra / MapLie

LieAlgebra / MapLie -- A quotient Lie algebra by the image of a map

Synopsis

Description

The program converts the elements f(x), where x is a generator in N, so that they will have type M=ambient(L) instead. The list of these converted elements may be looked upon by writing Q.relsLie. The Lie algebra Q is M modulo the ideal in M generated by the elements in Q.relsLie together with the induced differential on L.

i1 : M = lieAlgebra({a,b,c})

o1 = M

o1 : LieAlgebra
i2 : L = M/{a b}

o2 = L

o2 : LieAlgebra
i3 : N = lieAlgebra({d}, genWeights=>{2})

o3 = N

o3 : LieAlgebra
i4 : f = mapLie(L,N,{a c})

o4 = f

o4 : MapLie
i5 : Q = L/f

o5 = Q

o5 : LieAlgebra
i6 : Q.relsLie

o6 = { - (b a),  - (c a)}

o6 : List
i7 : Q1 = M/Q.relsLie

o7 = Q1

o7 : LieAlgebra
i8 : peekLie Q1

o8 = gensLie => {a, b, c}
     genWeights => {{1, 0}, {1, 0}, {1, 0}}
     genSigns => {0, 0, 0}
     relsLie => { - (b a),  - (c a)}
     genDiffs => {0, 0, 0}
     field => QQ
     diffl => false
     compdeg => 1
i9 : peekLie Q

o9 = gensLie => {a, b, c}
     genWeights => {{1, 0}, {1, 0}, {1, 0}}
     genSigns => {0, 0, 0}
     relsLie => { - (b a),  - (c a)}
     genDiffs => {0, 0, 0}
     field => QQ
     diffl => false
     compdeg => 1

See also