Pure braid group presentations via longest elements

Namanya, C. (2023) Pure braid group presentations via longest elements. Journal of Algebra, 628, pp. 1-21. (doi: 10.1016/j.jalgebra.2023.02.033)

Abstract

This paper gives a new, simplified presentation of the classical pure braid group. The generators are given by the squares of the longest elements over connected subgraphs, and we prove that the only relations are either commutators or certain palindromic length 5 box relations. This presentation is motivated by twist functors in algebraic geometry, but the proof is entirely Coxeter-theoretic. We also prove that the analogous set does not generate for all Coxeter arrangements, which in particular answers a question of Donovan and Wemyss.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Namanya, Caroline
• Authors: Namanya, C.
• College/School: College of Science and Engineering > School of Mathematics and Statistics
• Journal Name: Journal of Algebra
• Publisher: Elsevier
• ISSN: 0021-8693
• ISSN (Online): 1090-266X
• Published Online: 28 March 2023
• Copyright Holders: Copyright © 2023 Elsevier Inc.
• First Published: First published in Journal of Algebra 628: 1-21
• Publisher Policy: Reproduced in accordance with the publisher copyright policy