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GradedLieAlgebras :: RingElement LieDerivation

RingElement LieDerivation -- multiplication of a field element and a derivation

Synopsis

Description

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 $d: M\ \to\ L$. 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, see Number LieDerivation.

i1 : F = toField(ZZ/7[x]/{x^2+1})

o1 = F

o1 : PolynomialRing
i2 : M = lieAlgebra({a,b},Field=>F)

o2 = M

o2 : LieAlgebra
i3 : L = lieAlgebra({a,b},Field=>F)

o3 = L

o3 : LieAlgebra
i4 : f = map(L,M,{x a,3 b})

o4 = f

o4 : LieAlgebraMap
i5 : d = lieDerivation(f,{-x b,-2 a})

o5 = d

o5 : LieDerivation
i6 : describe (3*x) d

o6 = a => (3)b
     b => (x)a
     map => f
     sign => 0
     weight => {0, 0}
     source => M
     target => L

See also