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GradedLieAlgebras :: idealLie

idealLie -- computes the dimensions of a Lie ideal

Synopsis

Description

When the first argument is an integer, then the dimensions up to that degree are given. When the first argument is a list, then the dimension in that specific multidegree is given. Observe that if the Lie algebra has no differential, then an extra homological degree=0 is added to the given weights of the generators.

i1 : L = lieAlgebra({a,b,c},{[c,a]},genSigns=>{1,0,1},genWeights=>{{1,0},{1,0},{1,2}})

o1 = L

o1 : LieAlgebra
i2 : computeLie 5

o2 = {3, 4, 5, 12, 24}

o2 : List
i3 : d=defLie(mb_{4,5}+2*mb_{4,6})

o3 = {{1, 2}, {[c, b, b, a], [b, c, b, a]}}

o3 : List
i4 : idealLie(5,{[a,a],d})

o4 = {0, 1, 1, 4, 11}

o4 : List
i5 : idealLie({5,4,0},{[a,a],d})

o5 = 2

Below is shown a way to construct the quotient Lie algebra Q=L/I, where I is the ideal generated by [a,a] and d defined above.

i6 : Q=lieAlgebra({a,b,c},{[c,a],[a,a],d},genSigns=>{1,0,1},genWeights=>{{1,0},{1,0},{1,2}})

o6 = Q

o6 : LieAlgebra
i7 : computeLie 5

o7 = {3, 3, 4, 8, 13}

o7 : List

See also

Ways to use idealLie :