adjoint: The adjoint map

In RobinHankin/onion: Octonions and Quaternions

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]]

RobinHankin/onion documentation built on Feb. 17, 2025, 7:31 a.m.