intertwiner

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

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

Revised on February 3, 2013 21:34:53
by Urs Schreiber
(89.204.153.115)