Lie ring acts as derivations by adjoint action
From Groupprops
Statement
Let be a Lie ring. For any
, define the map:
given by:
(this is termed the left adjoint action by ).
Then, the following are true:
- For every
,
is a derivation of
(a derivation arising this way is termed an inner derivation).
- The map from
to the Lie ring of derivations of
, that sends an element
to the derivation
, is a homomorphism of Lie rings.