# 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:

## 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