# LieAlgebra / LieAlgebraMap -- make a quotient Lie algebra

## Synopsis

• Operator: /
• Usage:
Q=L/f
• Inputs:
• Outputs:
• Q, an instance of the type LieAlgebra, the quotient of $L$ by the ideal generated by the image of the map $f$

## Description

This is the same as $L$ modulo the set of values of $f$ applied to the generators of the source of $f$.

 i1 : M = lieAlgebra{a,b,c} o1 = M o1 : LieAlgebra i2 : L = M/{a b} o2 = L o2 : LieAlgebra i3 : N = lieAlgebra({d}, Weights=>{2}) o3 = N o3 : LieAlgebra i4 : f = map(L,N,{a c}) o4 = f o4 : LieAlgebraMap i5 : Q = L/f o5 = Q o5 : LieAlgebra i6 : describe Q o6 = generators => {a, b, c} Weights => {{1, 0}, {1, 0}, {1, 0}} Signs => {0, 0, 0} ideal => { - (b a), - (c a)} ambient => M diff => {} Field => QQ computedDegree => 0