@article{5999,
abstract = {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. },
author = {Yang, Yaping and Zhao, Gufang},
issn = {0024-6115},
journal = {Proceedings of the London Mathematical Society},
number = {5},
pages = {1029--1074},
publisher = {Oxford University Press (OUP)},
title = {{The cohomological Hall algebra of a preprojective algebra}},
doi = {10.1112/plms.12111},
volume = {116},
year = {2018},
}