Simply laced root system

An irreducible root system is simply laced when all roots have the same length, equivalently when its Dynkin diagram has only single edges. This is also equivalent towhenever $\alpha \ne \pm \beta$.

The connected positive-definite simply-laced Dynkin diagrams are $A_n$ for $n\ge 1$, $D_n$ for $n\ge 4$, and the exceptional diagrams $E_6,E_7,E_8$.