{"title":"-1的平方根的分类","authors":"Yin Tian","doi":"10.4064/FM232-1-7","DOIUrl":null,"url":null,"abstract":"We give a graphical calculus for a monoidal DG category $\\cal{I}$ whose Grothendieck group is isomorphic to the ring $\\mathbb{Z}[\\sqrt{-1}]$. We construct a categorical action of $\\cal{I}$ which lifts the action of $\\mathbb{Z}[\\sqrt{-1}]$ on $\\mathbb{Z}^2$.","PeriodicalId":309711,"journal":{"name":"arXiv: K-Theory and Homology","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2014-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"A categorification of the square root of -1\",\"authors\":\"Yin Tian\",\"doi\":\"10.4064/FM232-1-7\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We give a graphical calculus for a monoidal DG category $\\\\cal{I}$ whose Grothendieck group is isomorphic to the ring $\\\\mathbb{Z}[\\\\sqrt{-1}]$. We construct a categorical action of $\\\\cal{I}$ which lifts the action of $\\\\mathbb{Z}[\\\\sqrt{-1}]$ on $\\\\mathbb{Z}^2$.\",\"PeriodicalId\":309711,\"journal\":{\"name\":\"arXiv: K-Theory and Homology\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2014-11-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: K-Theory and Homology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4064/FM232-1-7\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: K-Theory and Homology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4064/FM232-1-7","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We give a graphical calculus for a monoidal DG category $\cal{I}$ whose Grothendieck group is isomorphic to the ring $\mathbb{Z}[\sqrt{-1}]$. We construct a categorical action of $\cal{I}$ which lifts the action of $\mathbb{Z}[\sqrt{-1}]$ on $\mathbb{Z}^2$.
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