# nLab intertwiner

## Idea

The term intertwiner is a synonym for homomorphism of representations/actions/modules.

Notably for linear representations $\rho_1$, $\rho_2$ of some group or associative algebra $A$ on vector spaces $V_1, V_2$, a linear map $u : V_1 \to V_2$ is said to intertwine $\rho_1$ with $\rho_2$ if for all $a \in A$ we have that

$u \circ \rho_1(a) = \rho_2(a)\circ u \,.$

Last revised on August 15, 2018 at 11:54:36. See the history of this page for a list of all contributions to it.