Braid groups and quiver mutation

Grant, Joseph and Marsh, Robert J. (2017) Braid groups and quiver mutation. Pacific Journal of Mathematics, 290 (1). pp. 77-116. ISSN 0030-8730

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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.

Item Type: Article
Uncontrolled Keywords: mutation,braid groups,cluster algebras,ginzburg dg algebra,spherical twist
Faculty \ School: Faculty of Science > School of Mathematics
UEA Research Groups: Faculty of Science > Research Groups > Algebra and Combinatorics
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Depositing User: Pure Connector
Date Deposited: 15 Mar 2017 01:41
Last Modified: 12 May 2023 02:30
DOI: 10.2140/pjm.2017.290.77


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