---- > [!definition] Definition. ([[abelian Lie algebra]]) > An **abelian Lie algebra** $\mathfrak{g}$ is one for which $[x,y]=0$ for all $x,y \in \mathfrak{g}$. ^definition > [!note] Remark. > So-named because this is equivalent to bracket [[abelian group|commuting]]. ^note ---- #### ---- #### 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 > ```