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

Synopsis

Usage:

L = lieAlgebra(gen,Signs => s)
Inputs:
- gen, a list, the list of generators
- s, a list, of signs (0 or 1), s has the same length as gen
- s, an integer, 0 or 1, the same sign is assigned to each generator
Outputs:
- L, an instance of the type 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 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

Further information

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

Functions with optional argument named Signs :