---- > [!definition] Definition. ([[orthogonal Lie algebra representation]]) > Let $V$ be a [[Lie algebra representation|representation]] of a [[Lie algebra]] $\mathfrak{g}$. We say $V$ is **orthogonal** if there exists a [[nondegenerate bilinear form|nondegenerate]] [[symmetric multilinear map|symmetric]] [[invariant bilinear form on a Lie algebra representation|invariant]] form on $V$. ^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 > ```