{"title":"$3$发生器上fomo - kirillov代数的Hochschild和循环(co)同调","authors":"Estanislao Herscovich, Ziling Li","doi":"10.4171/jncg/525","DOIUrl":null,"url":null,"abstract":"The goal of this article is to explicitly compute the Hochschild (co)homology of the Fomin–Kirillov algebra on three generators over a field of characteristic different from $2$ and $3$. We also obtain the cyclic (co)homology of the Fomin–Kirillov algebra in case the characteristic of the field is zero. Moreover, we compute the algebra structure of the Hochschild cohomology.","PeriodicalId":54780,"journal":{"name":"Journal of Noncommutative Geometry","volume":"29 1","pages":"0"},"PeriodicalIF":0.7000,"publicationDate":"2023-10-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Hochschild and cyclic (co)homology of the Fomin–Kirillov algebra on $3$ generators\",\"authors\":\"Estanislao Herscovich, Ziling Li\",\"doi\":\"10.4171/jncg/525\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The goal of this article is to explicitly compute the Hochschild (co)homology of the Fomin–Kirillov algebra on three generators over a field of characteristic different from $2$ and $3$. We also obtain the cyclic (co)homology of the Fomin–Kirillov algebra in case the characteristic of the field is zero. Moreover, we compute the algebra structure of the Hochschild cohomology.\",\"PeriodicalId\":54780,\"journal\":{\"name\":\"Journal of Noncommutative Geometry\",\"volume\":\"29 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2023-10-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Noncommutative Geometry\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4171/jncg/525\",\"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 Noncommutative Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4171/jncg/525","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
Hochschild and cyclic (co)homology of the Fomin–Kirillov algebra on $3$ generators
The goal of this article is to explicitly compute the Hochschild (co)homology of the Fomin–Kirillov algebra on three generators over a field of characteristic different from $2$ and $3$. We also obtain the cyclic (co)homology of the Fomin–Kirillov algebra in case the characteristic of the field is zero. Moreover, we compute the algebra structure of the Hochschild cohomology.
期刊介绍：
The Journal of Noncommutative Geometry covers the noncommutative world in all its aspects. It is devoted to publication of research articles which represent major advances in the area of noncommutative geometry and its applications to other fields of mathematics and theoretical physics. Topics covered include in particular:
Hochschild and cyclic cohomology
K-theory and index theory
Measure theory and topology of noncommutative spaces, operator algebras
Spectral geometry of noncommutative spaces
Noncommutative algebraic geometry
Hopf algebras and quantum groups
Foliations, groupoids, stacks, gerbes
Deformations and quantization
Noncommutative spaces in number theory and arithmetic geometry
Noncommutative geometry in physics: QFT, renormalization, gauge theory, string theory, gravity, mirror symmetry, solid state physics, statistical mechanics.
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