Curves in the disc, the type braid group, and a type zigzag algebra
Edmund Heng
The Australian National University, Acton Act, AustraliaKie Seng Nge
Xiamen University Malaysia, Sepang, Malaysia; The Australian National University, Acton Act, Australia
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Abstract
We construct a finite-dimensional quiver algebra from the non-simply laced type Dynkin diagram, which we call type zigzag algebra. This leads to a faithful categorical action of the type Artin (braid) group , acting on the homotopy category of its projective modules. This categorical action is also closely related to the topological action of , viewed as mapping class group of the punctured disc – hence, our exposition can be seen as a type analogue of Khovanov–Seidel's work.
Cite this article
Edmund Heng, Kie Seng Nge, Curves in the disc, the type braid group, and a type zigzag algebra. Quantum Topol. 15 (2024), no. 2, pp. 337–417
DOI 10.4171/QT/198