The symbol SPACE is used as notation for multiplication by scalars. The scalars belong to L#Field, which must be the same as M#Field, where \ $f: M\ \to\ L$. If the field is not QQ, then the scalars are of type RingElement. If the field is QQ, then the scalars are of type Number.
i1 : F = toField(ZZ/7[x]/{x^2+1})
o1 = F
o1 : PolynomialRing
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i2 : M = lieAlgebra({a,b},Field=>F)
o2 = M
o2 : LieAlgebra
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i3 : L = lieAlgebra({a,b},Field=>F)
o3 = L
o3 : LieAlgebra
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i4 : f = map(L,M,{x a,3 b})
o4 = f
o4 : LieAlgebraMap
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i5 : describe((3*x) f)
o5 = a => (-3)a
b => (2*x*1)b
source => M
target => L
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