next | previous | forward | backward | up | top | index | toc | Macaulay2 web site
GradedLieAlgebras :: weight

weight -- the weight of a derivation

Synopsis

Description

A derivation d:M->L has a weight which is the difference between the weight of any non-zero output and a non-zero input. The weight of the zero derivation is defined as {0,...,0} with as many zeroes as the length of weightLie(x) for any x in M or L. The weight is obtained as d.weight and may be seen using peekLie d.

i1 : L=lieAlgebra{a,b}/{a a a b,b b b a}

o1 = L

o1 : LieAlgebra
i2 : M=lieAlgebra({a1,b1},genWeights=>{3,3})

o2 = M

o2 : LieAlgebra
i3 : useLie L

o3 = L

o3 : LieAlgebra
i4 : f=mapLie(L,M,{a a b,b b a})

o4 = f

o4 : MapLie
i5 : d=derLie(f,{a,b})

o5 = d

o5 : DerLie
i6 : peekLie d

o6 = a1 => a
     b1 => b
     maplie => MapLie{a1 =>  - (a b a)}
                      b1 => (b b a)
                      sourceLie => M
                      targetLie => L
     sign => 0
     weight => {-2, 0}
     sourceLie => M
     targetLie => L
i7 : d.weight

o7 = {-2, 0}

o7 : List

See also

For the programmer

The object weight is a symbol.