Abstract
We describe presentations of braid groups of type ADE and show how these presentations are compatible with mutation of quivers, building on work of Barot and Marsh for Coxeter groups. In types A and D these presentations can be understood geometrically using triangulated surfaces. We then give a categorical interpretation of the presentations, with the new generators acting as spherical twists at simple modules on derived categories of Ginzburg dg-algebras of quivers with potential.
Original language | English |
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Pages (from-to) | 77-116 |
Number of pages | 40 |
Journal | Pacific Journal of Mathematics |
Volume | 290 |
Issue number | 1 |
DOIs | |
Publication status | Published - 7 Jul 2017 |
Keywords
- mutation
- braid groups
- cluster algebras
- Ginzburg dg algebra
- spherical twist
Profiles
-
Joseph Grant
- School of Engineering, Mathematics and Physics - Lecturer in Pure Mathematics
- Algebra and Combinatorics - Member
Person: Research Group Member, Academic, Teaching & Research