Twisted quantum loop algebras via semi-derived Ringel-Hall algebras

Twisted quantum loop algebras are a generalization of twisted quantum affine algebras in Drinfeld new presentation. The Hall algebras of Geigle–Lenzing’s weighted projective lines are used to realize (untwisted) quantum loop algebras of simply-laced type associated to star-shaped graphs by Schiffmann and Dou–Jiang–Xiao. In this paper, we use the semi-derived Ringel-Hall algebras of more general weighted projective lines to realize the twisted quantum loop algebras associated to the valued star-shaped graphs, including the twisted quantum affine algebras in Drinfeld new presentation.