---- > [!definition] Definition. ([[algebra subrepresentation]]) > Let $A$ be a (unital associative) [[algebra]] and $V$ a [[representation of an algebra|representation]] of $A$. We call a [[linear subspace]] $W \subset V$ an **algebra subrepresentation** of $V$ if the action of $A$ restricts to $W$, i.e., if $a \cdot w \in w \text{ for all } a \in A, w \in W.$ ^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 > ```