---- > [!definition] Definition. ([[center of a Lie algebra]]) > Let $\mathbb{F}$ be a [[field]]. The **center** of a [[Lie algebra]] $\mathfrak{g}$ over $\mathbb{F}$ is given by $\{ x \in \mathfrak{g} : [x,y]=0 \text{ for all } y \in \mathfrak{g} \},$ > i.e., the [[kernel]] of the [[adjoint representation]] $\mathfrak{g} \to \mathfrak{gl}(\mathfrak{g})$. ^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 > ```