# RingElement LieElement -- multiplication of a field element and a Lie element

## Synopsis

• Operator: SPACE
• Usage:
y = a x
• Inputs:
• a, , $a$ is an element in L#Field, where $L$ is of type Lielgebra
• x, an instance of the type LieElement, $x$ is of type $L$
• Outputs:
• y, an instance of the type LieElement, $y$ is of type $L$, the product $a*x$

## Description

The symbol SPACE is used as notation for multiplication by scalars. The scalars belong to L#Field. If the field is not QQ, then the scalars are of type RingElement. If the field is QQ, then the scalars are of type Number. If the field is not a prime field, then sometimes it is necessary to define the field outside the constructor lieAlgebra. Observe also that it is necessary to use the function toField when $F$ is defined as an algebraic extension of a prime field.

 i1 : F = toField(ZZ/7[x]/{x^2+1}) o1 = F o1 : PolynomialRing i2 : L = lieAlgebra({a,b},Field=>F) o2 = L o2 : LieAlgebra i3 : (3*x+2) a b + (2*x+3) b a o3 = (-x+1)(b a) o3 : L