---- > [!definition] Definition. ([[quotient Lie algebra]]) > Let $\mathfrak{g}$ be a [[Lie algebra]] and $I \subset \mathfrak{g}$ an [[ideal]]. Then the [[quotient module|quotient vector space]] $\mathfrak{g} / I$ naturally carries the structure of a [[Lie algebra]] via the bracket $[x + I, y+I]:=[x,y]+I.$ ([[universal property]]) ^definition ---- #### ---- #### 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 > ```