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