----- > [!proposition] Proposition. ([[the killing form includes into the ambient Lie algebra]]) > Let $\mathfrak{g}$ be a [[Lie algebra]] and $I \subset \mathfrak{g}$ an [[ideal of a Lie algebra|ideal]] of $\mathfrak{g}$. Denote by $\kappa_{I}$ the [[killing form]] of $I$ and by $\kappa$ the [[killing form]] on all of $\mathfrak{g}$ > Then $\kappa(x,y)=\kappa_{I}(x,y)$ for all $x,y \in I$. ^proposition > [!proof]- Proof. ([[the killing form includes into the ambient Lie algebra]]) > (fun) ----- #### ---- #### 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 > ```