Cluster braid groups of Coxeter-Dynkin diagrams. (English) Zbl 07920042
Summary: Cluster exchange groupoids are introduced by King-Qiu as an enhancement of cluster exchange graphs to study stability conditions and quadratic differentials. In this paper, we introduce the cluster exchange groupoid for any finite Coxeter-Dynkin diagram \(\Delta\) and show that its fundamental group is isomorphic to the corresponding braid group associated with \(\Delta \).
MSC:
| 16Gxx | Representation theory of associative rings and algebras |
| 13Fxx | Arithmetic rings and other special commutative rings |
| 20Fxx | Special aspects of infinite or finite groups |
Keywords:
braid groups; cluster exchange groupoids; Coxeter-Dynkin diagrams; generalized associahedronReferences:
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