---- > [!definition] Definition. ([[completely reducible]]) > A [[Lie algebra representation|representation]] $V$ (of a [[Lie algebra]], [[group]], etc.) is called **completely reducible** if $V=V_{1} \oplus \dots \oplus V_{n}$ for each $V_{i}$ [[irreducible Lie algebra representation|irreducible]]. ^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 > ```