adjoint {freealg}

The adjoint map

Description

The adjoint \(\mathrm{ad}_X\) of \(X\) is a map from a Lie group \(G\) to the endomorphism group of \(G\) defined by

\[\mathrm{ad}_X(Y)=\left[X,Y\right]\]

Usage

ad(x)

Arguments

x

Object nominally of class freealg but other classes accepted where they make sense

Details

details here

Note

Vignette adjoint gives more description

Author(s)

Robin K. S. Hankin

Examples

x <- rfalg()
y <- rfalg()

f <- ad(x)
f(y)


f(f(y)) # [x,[x,y]]