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GradedLieAlgebras :: lieAlgebra(..., genWeights => ...)

lieAlgebra(..., genWeights => ...) -- optional argument for lieAlgebra

Synopsis

Description

This is an option to tell lieAlgebra to assign the given weights to the generators. A weight is a list of integers of a length, which is the same for all generators. The first degree (also just called the degree), see degLie, is positive and, if the Lie algebra has a differential (i.e., the option diffl is true), the last degree is the homological degree, which is non-negative and less than the first degree. If the Lie algebra has no differential (i.e., the option diffl is false), the program defines a differential to be 0 and adds a last degree 0 to the existing degrees. When the option is given as a list of integers n1,n2,..., which is not possible when the option diffl is true, then the program defines the weights for the generators to be {n1,0}, {n2,0},... . The default value is 1, which has the effect that all generators have degree {1,0}.

i1 : peekLie lieAlgebra({a,b},genWeights=>{{1,2},{2,3}})

o1 = gensLie => {a, b}
     genWeights => {{1, 2, 0}, {2, 3, 0}}
     genSigns => {0, 0}
     relsLie => {}
     genDiffs => {0, 0}
     field => QQ
     diffl => false
     compdeg => 0
i2 : peekLie lieAlgebra({a,b},genWeights=>{{2,1},{3,2}},diffl=>true)

o2 = gensLie => {a, b}
     genWeights => {{2, 1}, {3, 2}}
     genSigns => {0, 0}
     relsLie => {}
     genDiffs => {0, 0}
     field => QQ
     diffl => true
     compdeg => 0
i3 : peekLie lieAlgebra({a,b})

o3 = gensLie => {a, b}
     genWeights => {{1, 0}, {1, 0}}
     genSigns => {0, 0}
     relsLie => {}
     genDiffs => {0, 0}
     field => QQ
     diffl => false
     compdeg => 0
i4 : peekLie lieAlgebra({a,b},genWeights=>{{1,0},{1,0}})

o4 = gensLie => {a, b}
     genWeights => {{1, 0, 0}, {1, 0, 0}}
     genSigns => {0, 0}
     relsLie => {}
     genDiffs => {0, 0}
     field => QQ
     diffl => false
     compdeg => 0
i5 : peekLie lieAlgebra({a,b},genWeights=>{{1,0},{1,0}},diffl=>true)

o5 = gensLie => {a, b}
     genWeights => {{1, 0}, {1, 0}}
     genSigns => {0, 0}
     relsLie => {}
     genDiffs => {0, 0}
     field => QQ
     diffl => true
     compdeg => 0
i6 : peekLie lieAlgebra({a,b},genWeights=>{1,2})

o6 = gensLie => {a, b}
     genWeights => {{1, 0}, {2, 0}}
     genSigns => {0, 0}
     relsLie => {}
     genDiffs => {0, 0}
     field => QQ
     diffl => false
     compdeg => 0

Further information

See also