# LieElement LieElement -- multiplication of Lie elements

## Synopsis

• Operator: SPACE
• Usage:
u=x y
• Inputs:
• x, an instance of the type LieElement, $x$ is of type $L$, where $L$ is of type LieAlgebra
• y, an instance of the type LieElement, $y$ is of type $L$
• Outputs:
• u, an instance of the type LieElement, $u$ is of type $L$, the Lie product of $x$ and $y$

## Description

SPACE is used as infix notation for the Lie multiplication. It is right associative and hence \break b b b a is the same as (b (b (b a))), which in output is written as (b b b a) or a normal form equivalent.

 i1 : L = lieAlgebra{a,b,c} o1 = L o1 : LieAlgebra i2 : b b b a o2 = (b b b a) o2 : L i3 : (a b+b c) (a c) o3 = (a c b a) - (b c c a) - (c a b a) + (c b c a) o3 : L