Self-derivation-invariant Lie subring

From Groupprops
Jump to: navigation, search
BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
This article describes a Lie subring property: a property that can be evaluated for a subring of a Lie ring
View a complete list of such properties
VIEW RELATED: Lie subring property implications | Lie subring property non-implications | Lie subring metaproperty satisfactions | Lie subring metaproperty dissatisfactions | Lie subring property satisfactions |Lie subring property dissatisfactions

Definition

A Lie subring A of a Lie ring L is termed a self-derivation-invariant Lie subring if the following holds. Consider a map d:A \to L that is a derivation from the Lie subring to the whole Lie ring viewed as a module over it. Then, d(A) \subseteq A.

Relation with other properties

Weaker properties

Facts