Definition:Linear Representation/Algebra
Jump to navigation
Jump to search
Definition
Let $K$ be a field.
Let $A$ be an associative unitary algebra over $K$.
Then a (linear) representation of $A$ is a vector space $V$ over $K$ equipped with a homomorphism of algebras:
- $\rho: A \to \map {\operatorname {End} } V$
where $\map {\operatorname {End} } V$ is the endomorphism ring of $V$.