{"title":"椭圆霍尔代数的分类","authors":"Youssef Mousaaid, Alistair Savage","doi":"10.4171/dm/896","DOIUrl":null,"url":null,"abstract":"We show that the central charge k reduction of the universal central extension of the elliptic Hall algebra is isomorphic to the trace, or zeroth Hochschild homology, of the quantum Heisenberg category of central charge k. As an application, we construct large families of representations of the universal extension of the elliptic Hall algebra.","PeriodicalId":50567,"journal":{"name":"Documenta Mathematica","volume":"35 1","pages":""},"PeriodicalIF":0.9000,"publicationDate":"2021-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Categorification of the elliptic Hall algebra\",\"authors\":\"Youssef Mousaaid, Alistair Savage\",\"doi\":\"10.4171/dm/896\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that the central charge k reduction of the universal central extension of the elliptic Hall algebra is isomorphic to the trace, or zeroth Hochschild homology, of the quantum Heisenberg category of central charge k. As an application, we construct large families of representations of the universal extension of the elliptic Hall algebra.\",\"PeriodicalId\":50567,\"journal\":{\"name\":\"Documenta Mathematica\",\"volume\":\"35 1\",\"pages\":\"\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2021-04-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Documenta Mathematica\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4171/dm/896\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Documenta Mathematica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/dm/896","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
We show that the central charge k reduction of the universal central extension of the elliptic Hall algebra is isomorphic to the trace, or zeroth Hochschild homology, of the quantum Heisenberg category of central charge k. As an application, we construct large families of representations of the universal extension of the elliptic Hall algebra.
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