[{"type":"journal_article","department":[{"_id":"TaHa"}],"external_id":{"arxiv":["1407.7994"]},"user_id":"3E5EF7F0-F248-11E8-B48F-1D18A9856A87","publication_identifier":{"issn":["0024-6115"]},"page":"1029-1074","abstract":[{"text":"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.\r\nWe 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. ","lang":"eng"}],"citation":{"chicago":"Yang, Yaping, and Gufang Zhao. “The Cohomological Hall Algebra of a Preprojective Algebra.” *Proceedings of the London Mathematical Society* 116, no. 5 (2018): 1029–74. https://doi.org/10.1112/plms.12111.","mla":"Yang, Yaping, and Gufang Zhao. “The Cohomological Hall Algebra of a Preprojective Algebra.” *Proceedings of the London Mathematical Society*, vol. 116, no. 5, Oxford University Press (OUP), 2018, pp. 1029–74, doi:10.1112/plms.12111.","ieee":"Y. Yang and G. Zhao, “The cohomological Hall algebra of a preprojective algebra,” *Proceedings of the London Mathematical Society*, vol. 116, no. 5, pp. 1029–1074, 2018.","short":"Y. Yang, G. Zhao, Proceedings of the London Mathematical Society 116 (2018) 1029–1074.","ama":"Yang Y, Zhao G. The cohomological Hall algebra of a preprojective algebra. *Proceedings of the London Mathematical Society*. 2018;116(5):1029-1074. doi:10.1112/plms.12111","ista":"Yang Y, Zhao G. 2018. The cohomological Hall algebra of a preprojective algebra. Proceedings of the London Mathematical Society. 116(5), 1029–1074.","apa":"Yang, Y., & Zhao, G. (2018). The cohomological Hall algebra of a preprojective algebra. *Proceedings of the London Mathematical Society*, *116*(5), 1029–1074. https://doi.org/10.1112/plms.12111"},"status":"public","date_created":"2019-02-14T13:14:22Z","volume":116,"title":"The cohomological Hall algebra of a preprojective algebra","year":"2018","date_published":"2018-05-01T00:00:00Z","oa":1,"doi":"10.1112/plms.12111","issue":"5","publication":"Proceedings of the London Mathematical Society","publication_status":"published","_id":"5999","language":[{"iso":"eng"}],"author":[{"first_name":"Yaping","full_name":"Yang, Yaping","last_name":"Yang"},{"first_name":"Gufang","id":"2BC2AC5E-F248-11E8-B48F-1D18A9856A87","last_name":"Zhao","full_name":"Zhao, Gufang"}],"intvolume":" 116","publisher":"Oxford University Press (OUP)","date_updated":"2019-08-02T12:39:07Z","day":"01","month":"05","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1407.7994"}],"quality_controlled":"1","oa_version":"Preprint"}]