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GradedLieAlgebras :: sign

sign -- the sign of a derivation

Synopsis

Description

A derivation d:M->L has a sign which is the difference modulo 2 between the sign of any non-zero output and a non-zero input. The sign of the zero derivation is defined as 0. The sign is obtained as d.sign and may be seen using peekLie d.

i1 : L=lieAlgebra({a,b},genSigns=>1)/{a a a b,b b b a}

o1 = L

o1 : LieAlgebra
i2 : M=lieAlgebra({a1,b1},genWeights=>{3,3},genSigns=>1)

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,b b})

o5 = d

o5 : DerLie
i6 : peekLie d

o6 = a1 => (b a)
     b1 => (b b)
     maplie => MapLie{a1 =>  - (1/2)(b a a)}
                      b1 => (b b a)
                      sourceLie => M
                      targetLie => L
     sign => 1
     weight => {-1, 0}
     sourceLie => M
     targetLie => L
i7 : d.sign

o7 = 1

See also

For the programmer

The object sign is a symbol.