Vol. 290, No. 1, 2017

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ISSN: 0030-8730
Braid groups and quiver mutation

Joseph Grant and Robert J. Marsh

Vol. 290 (2017), No. 1, 77–116
Abstract

We describe presentations of braid groups of type ADE and show how these presentations are compatible with mutation of quivers. 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.

Keywords
mutation, braid groups, cluster algebras, Ginzburg dg algebra, spherical twist
Mathematical Subject Classification 2010
Primary: 13F60, 16G20, 20F36
Secondary: 16E35, 16E45, 18E30
Milestones
Received: 28 March 2016
Revised: 13 January 2017
Accepted: 22 February 2017
Published: 7 July 2017
Authors
Joseph Grant
School of Mathematics
University of East Anglia
Norwich Research Park
Norwich
NR4 7TJ
United Kingdom
Robert J. Marsh
School of Mathematics
University of Leeds
Leeds
LS2 9JT
United Kingdom