Grant, J and Marsh, RJ orcid.org/0000-0002-4268-8937 (2017) Braid groups and quiver mutation. Pacific Journal of Mathematics, 290 (1). pp. 77-116. ISSN 0030-8730
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2017 Mathematical Sciences Publishers. This is an author produced version of a paper published in Pacific Journal of Mathematics. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | mutation, braid groups, cluster algebras, Ginzburg dg algebra, spherical twist |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Pure Mathematics (Leeds) |
Funding Information: | Funder Grant number EPSRC EP/G007497/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 09 Mar 2017 13:12 |
Last Modified: | 16 Jan 2018 19:51 |
Status: | Published |
Publisher: | Mathematical Sciences Publishers |
Identification Number: | 10.2140/pjm.2017.290.77 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:113358 |