Categorical action of the extended braid group of affine type $A$

Agnès Gadbled (1) , Anne-Laure Thiel (2, 3, 4) , Emmanuel Wagner (2)

1 CMUP - Centro de Matemática - Universidade do Porto
2 IMB - Institut de Mathématiques de Bourgogne [Dijon]
3 Department of Mathematics [Uppsala]
4 Institut Mittag-Leffler

Using a quiver algebra of a double cyclic quiver, we construct a faithful categorical action of the extended braid group of affine type $A$ on its bounded homotopy category of finitely generated projective modules. The algebra is trigraded and we identify the trigraded dimensions of the space of morphisms of this category with intersection numbers coming from the topological origin of the group.

Mots clés: Categorical action; Quiver; Geometric intersection; Braid groups; Categorification

Domaines: Mathématiques [math]

Agnès Gadbled, Anne-Laure Thiel, Emmanuel Wagner. Categorical action of the extended braid group of affine type $A$. Communications in Contemporary Mathematics, 2017, 19 (03), ⟨10.1142/S0219199716500243⟩. ⟨hal-01549167⟩