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

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

Synopsis

Description

This is an option to tell lieAlgebra to assign the given "signs" to the generators, which are either zero (even) or one (odd). If the option is given the value 1, then all generators will be odd, the default value is that all generators are even. The signs affect the axioms of a Lie superalgebra, see axiomsLie. Use signLie to compute the sign of an arbitrary homogeneous Lie expression.

i1 : peekLie lieAlgebra({a,b})

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

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

o3 = gensLie => {a, b}
     genWeights => {{1, 0}, {1, 0}}
     genSigns => {1, 1}
     relsLie => {}
     genDiffs => {0, 0}
     field => QQ
     diffl => false
     compdeg => 0

Further information

See also