adjoint {onion}

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 onion but other classes accepted where they make sense

Details

Here for completeness really.

Author(s)

Robin K. S. Hankin

Examples

x <- rquat()
y <- rquat()

f <- ad(x)
f(y)

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