[{"issue":"5","publisher":"Oxford University Press","publication_identifier":{"issn":["0024-6115"]},"scopus_import":"1","type":"journal_article","department":[{"_id":"TaHa"}],"day":"01","publication_status":"published","page":"1029-1074","intvolume":" 116","oa_version":"Preprint","citation":{"apa":"Yang, Y., & Zhao, G. (2018). The cohomological Hall algebra of a preprojective algebra. *Proceedings of the London Mathematical Society*. Oxford University Press. https://doi.org/10.1112/plms.12111","chicago":"Yang, Yaping, and Gufang Zhao. “The Cohomological Hall Algebra of a Preprojective Algebra.” *Proceedings of the London Mathematical Society*. Oxford University Press, 2018. https://doi.org/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. Oxford University Press, pp. 1029–1074, 2018.","ista":"Yang Y, Zhao G. 2018. The cohomological Hall algebra of a preprojective algebra. Proceedings of the London Mathematical Society. 116(5), 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","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, 2018, pp. 1029–74, doi:10.1112/plms.12111.","short":"Y. Yang, G. Zhao, Proceedings of the London Mathematical Society 116 (2018) 1029–1074."},"status":"public","date_updated":"2021-04-16T11:58:59Z","publication":"Proceedings of the London Mathematical Society","year":"2018","doi":"10.1112/plms.12111","author":[{"first_name":"Yaping","last_name":"Yang","full_name":"Yang, Yaping"},{"first_name":"Gufang","id":"2BC2AC5E-F248-11E8-B48F-1D18A9856A87","full_name":"Zhao, Gufang","last_name":"Zhao"}],"main_file_link":[{"url":"https://arxiv.org/abs/1407.7994","open_access":"1"}],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","abstract":[{"lang":"eng","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. "}],"month":"05","external_id":{"arxiv":["1407.7994"]},"title":"The cohomological Hall algebra of a preprojective algebra","date_published":"2018-05-01T00:00:00Z","volume":116,"quality_controlled":"1","oa":1,"_id":"5999","language":[{"iso":"eng"}],"article_processing_charge":"No","date_created":"2019-02-14T13:14:22Z"}]