{"title":"生成分区的线性类别","authors":"Daniel Gromada, Moritz Weber","doi":"10.1215/21562261-2022-0028","DOIUrl":null,"url":null,"abstract":"We present an algorithm for approximating linear categories of partitions (of sets). We report on concrete computer experiments based on this algorithm and how we found new examples of compact matrix quantum groups (so called \"non-easy\" quantum groups) with it. This also led to further theoretical insights regarding the representation theory of such quantum groups. We interpret some of the new categories constructing anticommutative twists of quantum groups.","PeriodicalId":49149,"journal":{"name":"Kyoto Journal of Mathematics","volume":" ","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2019-03-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":"{\"title\":\"Generating linear categories of partitions\",\"authors\":\"Daniel Gromada, Moritz Weber\",\"doi\":\"10.1215/21562261-2022-0028\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present an algorithm for approximating linear categories of partitions (of sets). We report on concrete computer experiments based on this algorithm and how we found new examples of compact matrix quantum groups (so called \\\"non-easy\\\" quantum groups) with it. This also led to further theoretical insights regarding the representation theory of such quantum groups. We interpret some of the new categories constructing anticommutative twists of quantum groups.\",\"PeriodicalId\":49149,\"journal\":{\"name\":\"Kyoto Journal of Mathematics\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2019-03-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"6\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Kyoto Journal of Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1215/21562261-2022-0028\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Kyoto Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1215/21562261-2022-0028","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
We present an algorithm for approximating linear categories of partitions (of sets). We report on concrete computer experiments based on this algorithm and how we found new examples of compact matrix quantum groups (so called "non-easy" quantum groups) with it. This also led to further theoretical insights regarding the representation theory of such quantum groups. We interpret some of the new categories constructing anticommutative twists of quantum groups.
期刊介绍：
The Kyoto Journal of Mathematics publishes original research papers at the forefront of pure mathematics, including surveys that contribute to advances in pure mathematics.
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