The cohomological Hall algebra of a preprojective algebra
By Yaping Yang, Gufang Zhao. 2014
80 citations recorded by the source corpus.
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 [‘The elliptic Hall algebra and the K‐theory of the Hilbert scheme of A2 ’, Duke Math. J. 162 (2013) 279–366.]. 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 [Lusztig, ‘On the character of certain irreducible modular representations’, Represent. Theory 19 (2015) 3–8; Joint Seminar, Mathematical Sciences Research Institute, October 28, 2014].
Subfields: Discrete Mathematics and Combinatorics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/664ec46b8763f8ba1aee685b391401cb648dbf6b
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In Discrete Mathematics and Combinatorics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- The integrality conjecture and the cohomology of preprojective stacks (2016, background): “The extra equivariant parameters arising from the torus action on M(Q̃) are not considered in the original paper [28], but were introduced, for the particular cohomological Hall algebras we are considering, in [36] and [48, 49].”