next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
GradedLieAlgebras :: ambient(LieAlgebra)

ambient(LieAlgebra) -- the free underlying Lie algebra

Synopsis

Description

Relations in L are elements in ambient(L). When a quotient Lie algebra Q=L/I is constructed, then the elements in the list I must be of type L, but the program converts the relations so that they have type ambient(L) instead. This may be seen by looking at Q.relsLie.

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

o1 = M

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

o2 = L

o2 : LieAlgebra
i3 : a c

o3 =  - (c a)

o3 : L
i4 : Q = L/{a c}

o4 = Q

o4 : LieAlgebra
i5 : Q.relsLie

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

o5 : List
i6 : oo_1

o6 =  - (c a)

o6 : M