---- > [!definition] Definition. ([[characteristic ideal of a Lie algebra]]) > A **characteristic ideal** of a [[Lie algebra]] $\mathfrak{g}$ is a [[linear subspace]] $I \subset \mathfrak{g}$ such that $\delta(I) \subset I$ for all [[derivation|derivations]] $\delta$ of $\mathfrak{g}$. ^definition > [!example] > Every element in the [[derived and central series of a Lie algebra|derived]] and [[central series of a Lie algebra|central]] series of $\mathfrak{g}$ is a characteristic ideal. Indeed, it is easy to see that $[\mathfrak{g}, \mathfrak{g}]$ is a characteristic ideal and the higher-order terms build off this. ^example ---- #### ---- #### References > [!backlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM [[]] > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ``` > [!frontlink] > ```dataview > TABLE rows.file.link as "Further Reading" > FROM outgoing([[]]) > FLATTEN file.tags as Tag > WHERE Tag = "#definition" OR Tag = "#theorem" OR Tag = "#MOC" OR Tag = "#proposition" OR Tag = "#axiom" > GROUP BY Tag > ```