Let $k$ be an algebraically closed field of characteristic $0$. The assignment that sends a finite-dimensional semisimple Lie algebra $\mathfrak{g}$ over $k$ to the finite disjoint union of the Dynkin diagrams of its simple ideals induces a bijection
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\begin{align*}
\left\{
\begin{array}{c}
\text{isomorphism classes of finite-dimensional} \\
\text{semisimple Lie algebras over } k
\end{array}
\right\}
\longleftrightarrow
\left\{
\begin{array}{c}
\text{finite disjoint unions of connected} \\
\text{finite type Dynkin diagrams}
\end{array}
\right\}.
\end{align*}
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Equivalently, two finite-dimensional semisimple Lie algebras over $k$ are isomorphic if and only if their associated finite disjoint unions of Dynkin diagrams are isomorphic as finite disjoint unions of labeled Dynkin diagrams.