The cohomological Hall algebra of a preprojective algebra
Yang, Yaping
Zhao, Gufang
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 Press
2018
info:eu-repo/semantics/article
doc-type:article
text
http://purl.org/coar/resource_type/c_6501
https://research-explorer.app.ist.ac.at/record/5999
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>
eng
info:eu-repo/semantics/altIdentifier/doi/10.1112/plms.12111
info:eu-repo/semantics/altIdentifier/issn/0024-6115
info:eu-repo/semantics/altIdentifier/arxiv/1407.7994
info:eu-repo/semantics/openAccess