Let $(V_1,\rho_1)$ and $(V_2,\rho_2))$ be representations of the group $G$. The tensor product of $V_1$ and $V_2$ is a representation of $G$ over the tensor product of vector spaces $V_1\otimes V_2$ under the linear transformation $\rho_1\otimes \rho_2 = \rho:G\to V_1\otimes V_2$ such that $\rho(g)(v_1\otimes v_2) = (\rho_1(g)v_1)\otimes (\rho_2(g)v_2)$.
Wikidata ID: Q48995828