article
The cohomological Hall algebra of a preprojective algebra
published
yes
Yaping
Yang
author
Gufang
Zhao
author 2BC2AC5E-F248-11E8-B48F-1D18A9856A87
TaHa
department
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.
We 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.
Oxford University Press2018
eng
Proceedings of the London Mathematical Society
0024-6115
1407.799410.1112/plms.12111
11651029-1074
Yang, Yaping, and Gufang Zhao. “The Cohomological Hall Algebra of a Preprojective Algebra.” <i>Proceedings of the London Mathematical Society</i>, vol. 116, no. 5, Oxford University Press, 2018, pp. 1029–74, doi:<a href="https://doi.org/10.1112/plms.12111">10.1112/plms.12111</a>.
Y. Yang, G. Zhao, Proceedings of the London Mathematical Society 116 (2018) 1029–1074.
Yang Y, Zhao G. 2018. The cohomological Hall algebra of a preprojective algebra. Proceedings of the London Mathematical Society. 116(5), 1029–1074.
Yang Y, Zhao G. The cohomological Hall algebra of a preprojective algebra. <i>Proceedings of the London Mathematical Society</i>. 2018;116(5):1029-1074. doi:<a href="https://doi.org/10.1112/plms.12111">10.1112/plms.12111</a>
Y. Yang and G. Zhao, “The cohomological Hall algebra of a preprojective algebra,” <i>Proceedings of the London Mathematical Society</i>, vol. 116, no. 5. Oxford University Press, pp. 1029–1074, 2018.
Yang, Y., & Zhao, G. (2018). The cohomological Hall algebra of a preprojective algebra. <i>Proceedings of the London Mathematical Society</i>. Oxford University Press. <a href="https://doi.org/10.1112/plms.12111">https://doi.org/10.1112/plms.12111</a>
Yang, Yaping, and Gufang Zhao. “The Cohomological Hall Algebra of a Preprojective Algebra.” <i>Proceedings of the London Mathematical Society</i>. Oxford University Press, 2018. <a href="https://doi.org/10.1112/plms.12111">https://doi.org/10.1112/plms.12111</a>.
59992019-02-14T13:14:22Z2021-04-16T11:58:59Z