{"title":"伽罗瓦理论的量子化","authors":"A. Masuoka, Katsunori Saito, H. Umemura","doi":"10.5802/AFST.1663","DOIUrl":null,"url":null,"abstract":"This note is a development of our two previous papers, arXiv:1212.3392v1 and 1306.3660v1. \nThe fundamental question is whether there exists a Galois theory, in which the Galois group is a quantum group. \nFor a linear equations with respect to a Hopf algebra, we arrived at a final form if the base field consists of constants. In this case, we have non-commutative Picard-Vessiot rings and asymmetric Tannaka theory. \nFor non-linear equations there are examples that might make us optimistic.","PeriodicalId":169800,"journal":{"name":"Annales de la Faculté des sciences de Toulouse : Mathématiques","volume":"102 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2015-01-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"Toward quantization of Galois theory\",\"authors\":\"A. Masuoka, Katsunori Saito, H. Umemura\",\"doi\":\"10.5802/AFST.1663\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This note is a development of our two previous papers, arXiv:1212.3392v1 and 1306.3660v1. \\nThe fundamental question is whether there exists a Galois theory, in which the Galois group is a quantum group. \\nFor a linear equations with respect to a Hopf algebra, we arrived at a final form if the base field consists of constants. In this case, we have non-commutative Picard-Vessiot rings and asymmetric Tannaka theory. \\nFor non-linear equations there are examples that might make us optimistic.\",\"PeriodicalId\":169800,\"journal\":{\"name\":\"Annales de la Faculté des sciences de Toulouse : Mathématiques\",\"volume\":\"102 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2015-01-27\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Annales de la Faculté des sciences de Toulouse : Mathématiques\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5802/AFST.1663\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annales de la Faculté des sciences de Toulouse : Mathématiques","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5802/AFST.1663","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
This note is a development of our two previous papers, arXiv:1212.3392v1 and 1306.3660v1.
The fundamental question is whether there exists a Galois theory, in which the Galois group is a quantum group.
For a linear equations with respect to a Hopf algebra, we arrived at a final form if the base field consists of constants. In this case, we have non-commutative Picard-Vessiot rings and asymmetric Tannaka theory.
For non-linear equations there are examples that might make us optimistic.
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