homomorphism

《Introduction to Representation Theory》 · 第 23 页 · Section 2.9「Lie algebras」，Definition 2.9.6

Let $\mathfrak g_1,\mathfrak g_2$ be Lie algebras. A homomorphism of Lie algebras $\varphi:\mathfrak g_1\to\mathfrak g_2$ is a linear map such that $\varphi([a,b])=[\varphi(a),\varphi(b)]$.