[{"creator":{"login":"dernst","id":"2DF688A6-F248-11E8-B48F-1D18A9856A87"},"issue":"5","dc":{"language":["eng"],"description":["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. "],"identifier":["https://research-explorer.app.ist.ac.at/record/5999"],"relation":["info:eu-repo/semantics/altIdentifier/doi/10.1112/plms.12111","info:eu-repo/semantics/altIdentifier/issn/0024-6115","info:eu-repo/semantics/altIdentifier/arxiv/1407.7994"],"title":["The cohomological Hall algebra of a preprojective algebra"],"creator":["Yang, Yaping","Zhao, Gufang"],"type":["info:eu-repo/semantics/article","doc-type:article","text","http://purl.org/coar/resource_type/c_6501"],"rights":["info:eu-repo/semantics/openAccess"],"publisher":["Oxford University Press"],"source":["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"],"date":["2018"]},"publication_identifier":{"issn":[]},"scopus_import":"1","type":"journal_article","department":[{"tree":[{"_id":"ResearchGroups"},{"_id":"IST"}],"_id":"TaHa"}],"day":"01","intvolume":" 116","page":"1029-1074","oa_version":"Preprint","publication_status":"published","date_updated":"2021-04-16T11:58:59Z","publication":"Proceedings of the London Mathematical Society","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.” *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.","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.","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","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."},"status":"public","uri_base":"https://research-explorer.app.ist.ac.at","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","main_file_link":[{"url":"https://arxiv.org/abs/1407.7994","open_access":"1"}],"abstract":[{"lang":"eng"}],"author":[{"first_name":"Yaping","last_name":"Yang"},{"last_name":"Zhao","id":"2BC2AC5E-F248-11E8-B48F-1D18A9856A87","first_name":"Gufang"}],"external_id":{"arxiv":[]},"dini_type":"doc-type:article","month":"05","volume":116,"date_published":"2018-05-01T00:00:00Z","quality_controlled":"1","article_processing_charge":"No","_id":"5999","oa":1,"language":[{}],"date_created":"2019-02-14T13:14:22Z"}]