{"title":"戴恩金类型离散簇类的格罗内狄克群A∞","authors":"Dave Murphy","doi":"10.1016/j.jalgebra.2024.08.019","DOIUrl":null,"url":null,"abstract":"<div><p>In this work we compute the triangulated Grothendieck groups for each of the family of discrete cluster categories of Dynkin type <span><math><msub><mrow><mi>A</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span> as introduced by Holm-Jørgensen. Subsequently, we also compute the Grothendieck group of a completion of these discrete cluster categories in the sense of Paquette-Yildirim.</p></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0021869324004770/pdfft?md5=ce30e7abc9151705dc42c602e2425382&pid=1-s2.0-S0021869324004770-main.pdf","citationCount":"0","resultStr":"{\"title\":\"The Grothendieck groups of discrete cluster categories of Dynkin type A∞\",\"authors\":\"Dave Murphy\",\"doi\":\"10.1016/j.jalgebra.2024.08.019\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In this work we compute the triangulated Grothendieck groups for each of the family of discrete cluster categories of Dynkin type <span><math><msub><mrow><mi>A</mi></mrow><mrow><mo>∞</mo></mrow></msub></math></span> as introduced by Holm-Jørgensen. Subsequently, we also compute the Grothendieck group of a completion of these discrete cluster categories in the sense of Paquette-Yildirim.</p></div>\",\"PeriodicalId\":14888,\"journal\":{\"name\":\"Journal of Algebra\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2024-08-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0021869324004770/pdfft?md5=ce30e7abc9151705dc42c602e2425382&pid=1-s2.0-S0021869324004770-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Algebra\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0021869324004770\",\"RegionNum\":2,\"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":"Journal of Algebra","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021869324004770","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
The Grothendieck groups of discrete cluster categories of Dynkin type A∞
In this work we compute the triangulated Grothendieck groups for each of the family of discrete cluster categories of Dynkin type as introduced by Holm-Jørgensen. Subsequently, we also compute the Grothendieck group of a completion of these discrete cluster categories in the sense of Paquette-Yildirim.
期刊介绍：
The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.
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