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

Description

This is an option to tell lieAlgebra to assign the given "signs" to the generators, which are either 0 (even) or 1 (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 LieAlgebra. Use sign(LieElement) to compute the sign of an arbitrary homogeneous Lie expression.

i1 : describe lieAlgebra{a,b}

o1 = generators => {a, b}
     Weights => {{1, 0}, {1, 0}}
     Signs => {0, 0}
     ideal => {}
     ambient => LieAlgebra{...10...}
     diff => {}
     Field => QQ
     computedDegree => 0
 
i2 : describe lieAlgebra({a,b},Signs=>{1,0})

o2 = generators => {a, b}
     Weights => {{1, 0}, {1, 0}}
     Signs => {1, 0}
     ideal => {}
     ambient => LieAlgebra{...10...}
     diff => {}
     Field => QQ
     computedDegree => 0
 
i3 : describe lieAlgebra({a,b},Signs=>1)

o3 = generators => {a, b}
     Weights => {{1, 0}, {1, 0}}
     Signs => {1, 1}
     ideal => {}
     ambient => LieAlgebra{...10...}
     diff => {}
     Field => QQ
     computedDegree => 0

See also

Functions with optional argument named Signs:

Further information

  • Default value: 0
  • Function: lieAlgebra -- make a free Lie algebra
  • Option key: Signs -- name for an optional argument for lieAlgebra

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/GradedLieAlgebras/doc.m2:739:0.