RingElement LieAlgebraMap -- multiplication of a field element and a homomorphism

Synopsis

Operator: SPACE
Usage:

g = a f
Inputs:
- a, a ring element, $a$ is an element in L#Field, where $L$ is the target of $f$
- f, an instance of the type LieAlgebraMap,
Outputs:
- g, an instance of the type LieAlgebraMap,

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 \ $f: M\ \to\ L$. 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

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 : describe((3*x) f)

o5 = a => (-3)a
     b => (2*x*1)b
     source => M
     target => L

Ways to use this method: