---- > [!definition] Definition. ([[quotient representation]]) > Let $V$ be a [[Lie algebra representation]] of [[Lie algebra]] $\mathfrak{g}$. If $W \subset V$ is a [[Lie algebra representation]], then the [[quotient module|quotient space]] $V / W= \{ v+ W: v \in V \}$ is a $\mathfrak{g}$-representation via the action $x \cdot (v + W):= (x \cdot v)+W.$ ([[universal property]] as usual) ^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 > ```