# LieAlgebraMap -- the class of all Lie algebra homomorphisms

## Description

This type represents homomorphisms from $M$ to $L$, where $M$ and $L$ are Lie algebras defined over the same field. Use the constructor map(LieAlgebra,LieAlgebra,List) to define homomorphisms. A homomorphism is given by the value of the generators and it should preserve weight and sign. Observe that the zero element is considered to have any weight and sign. The zero element in L is denoted by 0_L. An object of type LieAlgebraMap need not be well defined as a map and need not commute with the differentials. Use isWellDefined(ZZ,LieAlgebraMap) to check if this is true.

 i1 : M = lieAlgebra({a,b,c},Weights=>{2,1,1}) o1 = M o1 : LieAlgebra i2 : L = lieAlgebra{a,b} o2 = L o2 : LieAlgebra i3 : f = map(L,M,{a b,a,0_L}) o3 = f o3 : LieAlgebraMap i4 : isWellDefined(3,f) the map is well defined for all degrees the map commutes with the differential for all degrees o4 = true i5 : describe f o5 = a => - (b a) b => a c => 0 source => M target => L i6 : use M i7 : f (a c - a b) o7 = - (a b a) o7 : L