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arXiv · 2606.19691

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

Ming Lu·Shiquan Ruan
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Abstract

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.

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Ming Lu, Shiquan Ruan. 2026-06-18. Twisted quantum loop algebras via semi-derived Ringel-Hall algebras. https://arxiv.org/abs/2606.19691

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