{"status":"public","_id":"5999","page":"1029-1074","publication":"Proceedings of the London Mathematical Society","author":[{"full_name":"Yang, Yaping","last_name":"Yang","first_name":"Yaping"},{"full_name":"Zhao, Gufang","last_name":"Zhao","first_name":"Gufang","id":"2BC2AC5E-F248-11E8-B48F-1D18A9856A87"}],"department":[{"_id":"TaHa"}],"date_created":"2019-02-14T13:14:22Z","date_updated":"2023-09-19T14:37:19Z","volume":116,"publication_identifier":{"issn":["0024-6115"]},"year":"2018","issue":"5","language":[{"iso":"eng"}],"scopus_import":"1","oa_version":"Preprint","publication_status":"published","month":"05","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. "}],"isi":1,"day":"01","main_file_link":[{"url":"https://arxiv.org/abs/1407.7994","open_access":"1"}],"publisher":"Oxford University Press","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","type":"journal_article","intvolume":"       116","title":"The cohomological Hall algebra of a preprojective algebra","oa":1,"quality_controlled":"1","external_id":{"arxiv":["1407.7994"],"isi":["000431506400001"]},"date_published":"2018-05-01T00:00:00Z","citation":{"ieee":"Y. Yang and G. Zhao, “The cohomological Hall algebra of a preprojective algebra,” <i>Proceedings of the London Mathematical Society</i>, vol. 116, no. 5. Oxford University Press, pp. 1029–1074, 2018.","ama":"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>","chicago":"Yang, Yaping, and Gufang Zhao. “The Cohomological Hall Algebra of a Preprojective Algebra.” <i>Proceedings of the London Mathematical Society</i>. Oxford University Press, 2018. <a href=\"https://doi.org/10.1112/plms.12111\">https://doi.org/10.1112/plms.12111</a>.","ista":"Yang Y, Zhao G. 2018. The cohomological Hall algebra of a preprojective algebra. Proceedings of the London Mathematical Society. 116(5), 1029–1074.","mla":"Yang, Yaping, and Gufang Zhao. “The Cohomological Hall Algebra of a Preprojective Algebra.” <i>Proceedings of the London Mathematical Society</i>, vol. 116, no. 5, Oxford University Press, 2018, pp. 1029–74, doi:<a href=\"https://doi.org/10.1112/plms.12111\">10.1112/plms.12111</a>.","short":"Y. Yang, G. Zhao, Proceedings of the London Mathematical Society 116 (2018) 1029–1074.","apa":"Yang, Y., &#38; Zhao, G. (2018). The cohomological Hall algebra of a preprojective algebra. <i>Proceedings of the London Mathematical Society</i>. Oxford University Press. <a href=\"https://doi.org/10.1112/plms.12111\">https://doi.org/10.1112/plms.12111</a>"},"doi":"10.1112/plms.12111","article_processing_charge":"No"}