Macaulay2 » Documentation
Packages » GradedLieAlgebras :: map(LieAlgebra,LieAlgebra)
next | previous | forward | backward | up | index | toc

map(LieAlgebra,LieAlgebra) -- make a natural Lie algebra homomorphism



The optional inputs given above are not relevant for Lie algebras. The effect of map(L,M) is that the "common" generators are mapped to themselves and the other generators are mapped to 0 (cf map for rings). Two generators are "common" if they have the same name and the same weight and sign. The output map f might not be well defined and not commute with the differentials. It can be checked whether this is true by using isWellDefined(ZZ,LieAlgebraMap).

i1 : M = lieAlgebra{a,b,c}

o1 = M

o1 : LieAlgebra
i2 : L = lieAlgebra({a,b,d},Weights=>{2,1,1})

o2 = L

o2 : LieAlgebra
i3 : f = map(L,M)

o3 = f

o3 : LieAlgebraMap
i4 : describe f

o4 = a => 0
     b => b
     c => 0
     source => M
     target => L

See also

Ways to use this method: