---
_id: '5999'
abstract:
- lang: eng
text: "We introduce for each quiver Q and each algebraic oriented cohomology theory
A, the cohomological Hall algebra (CoHA) of Q, as the A-homology of the moduli
of representations of the preprojective algebra of Q. This generalizes the K-theoretic
Hall algebra of commuting varieties defined by Schiffmann-Vasserot. When A is
the Morava K-theory, we show evidence that this algebra is a candidate for Lusztig's
reformulated conjecture on modular representations of algebraic groups.\r\nWe
construct an action of the preprojective CoHA on the A-homology of Nakajima quiver
varieties. We compare this with the action of the Borel subalgebra of Yangian
when A is the intersection theory. We also give a shuffle algebra description
of this CoHA in terms of the underlying formal group law of A. As applications,
we obtain a shuffle description of the Yangian. "
article_processing_charge: No
author:
- first_name: Yaping
full_name: Yang, Yaping
last_name: Yang
- first_name: Gufang
full_name: Zhao, Gufang
id: 2BC2AC5E-F248-11E8-B48F-1D18A9856A87
last_name: Zhao
citation:
ama: Yang Y, Zhao G. The cohomological Hall algebra of a preprojective algebra.
*Proceedings of the London Mathematical Society*. 2018;116(5):1029-1074.
doi:10.1112/plms.12111
apa: Yang, Y., & Zhao, G. (2018). The cohomological Hall algebra of a preprojective
algebra. *Proceedings of the London Mathematical Society*. Oxford University
Press. https://doi.org/10.1112/plms.12111
chicago: Yang, Yaping, and Gufang Zhao. “The Cohomological Hall Algebra of a Preprojective
Algebra.” *Proceedings of the London Mathematical Society*. Oxford University
Press, 2018. https://doi.org/10.1112/plms.12111.
ieee: Y. Yang and G. Zhao, “The cohomological Hall algebra of a preprojective algebra,”
*Proceedings of the London Mathematical Society*, vol. 116, no. 5. Oxford
University Press, pp. 1029–1074, 2018.
ista: Yang Y, Zhao G. 2018. The cohomological Hall algebra of a preprojective algebra.
Proceedings of the London Mathematical Society. 116(5), 1029–1074.
mla: Yang, Yaping, and Gufang Zhao. “The Cohomological Hall Algebra of a Preprojective
Algebra.” *Proceedings of the London Mathematical Society*, vol. 116, no.
5, Oxford University Press, 2018, pp. 1029–74, doi:10.1112/plms.12111.
short: Y. Yang, G. Zhao, Proceedings of the London Mathematical Society 116 (2018)
1029–1074.
date_created: 2019-02-14T13:14:22Z
date_published: 2018-05-01T00:00:00Z
date_updated: 2021-04-16T11:58:59Z
day: '01'
department:
- _id: TaHa
doi: 10.1112/plms.12111
external_id:
arxiv:
- '1407.7994'
intvolume: ' 116'
issue: '5'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/1407.7994
month: '05'
oa: 1
oa_version: Preprint
page: 1029-1074
publication: Proceedings of the London Mathematical Society
publication_identifier:
issn:
- 0024-6115
publication_status: published
publisher: Oxford University Press
quality_controlled: '1'
scopus_import: '1'
status: public
title: The cohomological Hall algebra of a preprojective algebra
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 116
year: '2018'
...