@article{7940,
abstract = {We prove that the Yangian associated to an untwisted symmetric affine Kac–Moody Lie algebra is isomorphic to the Drinfeld double of a shuffle algebra. The latter is constructed in [YZ14] as an algebraic formalism of cohomological Hall algebras. As a consequence, we obtain the Poincare–Birkhoff–Witt (PBW) theorem for this class of affine Yangians. Another independent proof of the PBW theorem is given recently by Guay, Regelskis, and Wendlandt [GRW18].},
author = {Yang, Yaping and Zhao, Gufang},
issn = {1531586X},
journal = {Transformation Groups},
publisher = {Springer Nature},
title = {{The PBW theorem for affine Yangians}},
doi = {10.1007/s00031-020-09572-6},
year = {2020},
}
@article{7004,
abstract = {We define an action of the (double of) Cohomological Hall algebra of Kontsevich and Soibelman on the cohomology of the moduli space of spiked instantons of Nekrasov. We identify this action with the one of the affine Yangian of gl(1). Based on that we derive the vertex algebra at the corner Wr1,r2,r3 of Gaiotto and Rapčák. We conjecture that our approach works for a big class of Calabi–Yau categories, including those associated with toric Calabi–Yau 3-folds.},
author = {Rapcak, Miroslav and Soibelman, Yan and Yang, Yaping and Zhao, Gufang},
issn = {1432-0916},
journal = {Communications in Mathematical Physics},
publisher = {Springer Nature},
title = {{Cohomological Hall algebras, vertex algebras and instantons}},
doi = {10.1007/s00220-019-03575-5},
year = {2019},
}
@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},
}