ADE classification

In mathematics, the ADE classification (originally A-D-E classifications) is the complete list of simply laced Dynkin diagrams or other mathematical objects satisfying analogous axioms; "simply laced" means that there are no multiple edges, which corresponds to all simple roots in the root system forming angles of ${\displaystyle \pi /2=90^{\circ }}$ (no edge between the vertices) or ${\displaystyle 2\pi /3=120^{\circ }}$ (single edge between the vertices). The list comprises

These comprise two of the four families of Dynkin diagrams (omitting ${\displaystyle B_{n}}$ and ${\displaystyle C_{n}}$), and three of the five exceptional Dynkin diagrams (omitting ${\displaystyle F_{4}}$ and ${\displaystyle G_{2}}$).

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