The critical CoHA of a quiver with potential

Davison, B. (2017) The critical CoHA of a quiver with potential. Quarterly Journal of Mathematics, 68(2), pp. 635-703. (doi: 10.1093/qmath/haw053)

Abstract

Pursuing the similarity between the Kontsevich–Soibelman construction of the cohomological Hall algebra (CoHA) of BPS states and Lusztig's construction of canonical bases for quantum enveloping algebras, and the similarity between the integrality conjecture for motivic Donaldson–Thomas invariants and the PBW theorem for quantum enveloping algebras, we build a coproduct on the CoHA associated to a quiver with potential. We also prove a cohomological dimensional reduction theorem, further linking a special class of CoHAs with Yangians, and explaining how to connect the study of character varieties with the study of CoHAs.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Davison, Nicholas
• Authors: Davison, B.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Quarterly Journal of Mathematics
• Publisher: Oxford University Press
• ISSN: 0033-5606
• ISSN (Online): 1464-3847
• Published Online: 06 February 2017
• Copyright Holders: Copyright © 2017 Oxford University Press
• First Published: First published in Quarterly Journal of Mathematics 68(2):635-703
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher