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
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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) | ||||
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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: | https://doi.org/10.2140/pjm.2017.290.77 |