---- > [!definition] Definition. ([[Lie subalgebra]]) > A **Lie subalgebra** of a [[Lie algebra]] $\mathfrak{g}$ is a [[linear subspace]] $\mathfrak{l} \subset \mathfrak{g}$ that is stable under the bracket, i.e., $[x,y]_{} \in \mathfrak{l} \text{ for all } x,y \in \mathfrak{l}.$ > By restricting the bracket $[-,-]_{\mathfrak{g}}$ to $\mathfrak{l}$, $\mathfrak{l}$ becomes a [[Lie algebra]]. ^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 > ```