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GradedLieAlgebras :: MapLie

MapLie -- a Type for homomorphisms of Lie algebras

Description

This Type represents homomorphisms f from M to L, where M and L are Lie algebras. Use the constructor mapLie 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 L.zz.

i1 : M = lieAlgebra({a,b,c},genWeights=>{2,1,1})

o1 = M

o1 : LieAlgebra
i2 : L = lieAlgebra{a,b}

o2 = L

o2 : LieAlgebra
i3 : f = mapLie(L,M,{a b,a,L.zz})

o3 = f

o3 : MapLie
i4 : peekLie f

o4 = MapLie{a =>  - (b a) }
            b => a
            c => 0
            sourceLie => M
            targetLie => L
i5 : useLie M

o5 = M

o5 : LieAlgebra
i6 : f (a c - a b)

o6 =  - (a b a)

o6 : L

See also

Functions and methods returning an object of class MapLie :

Methods that use an object of class MapLie :

For the programmer

The object MapLie is a type, with ancestor classes MutableHashTable < HashTable < Thing.