The cohomological Hall algebra of a preprojective algebra
| Autor: | Gufang Zhao, Yaping Yang |
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| Rok vydání: | 2018 |
| Předmět: |
Intersection theory
medicine.medical_specialty General Mathematics 010102 general mathematics Subalgebra Quiver Formal group 01 natural sciences Cohomology Shuffle algebra Algebra Hall algebra Mathematics::Quantum Algebra 0103 physical sciences medicine 010307 mathematical physics 0101 mathematics Yangian Mathematics::Representation Theory Mathematics |
| Zdroj: | Proceedings of the London Mathematical Society. 116:1029-1074 |
| ISSN: | 0024-6115 |
| DOI: | 10.1112/plms.12111 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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