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We associate a generalized root system in the sense of Kyoji Saito to anorbifold projective line via the derived category of finite dimensionalrepresentations of a certain bound quiver algebra. We generalize results bySaito--Takebayshi and Yamada for elliptic Weyl groups and elliptic Artin groupsto the Weyl groups and the fundamental groups of the regular orbit spacesassociated to the generalized root systems. Moreover we study the relationbetween this fundamental group and a certain subgroup of the autoequivalencegroup of a triangulated subcategory of the derived category of $2$-Calabi--Yaucompletion of the bound quiver algebra.

On Weyl Groups and Artin Groups Associated to Orbifold Projective Lines