{"title":"关于Lie-Rinehart超代数的分类和变形","authors":"Quentin Ehret, A. Makhlouf","doi":"10.46298/cm.10537","DOIUrl":null,"url":null,"abstract":"The purpose of this paper is to study Lie-Rinehart superalgebras over\ncharacteristic zero fields, which are consisting of a supercommutative\nassociative superalgebra $A$ and a Lie superalgebra $L$ that are compatible in\na certain way. We discuss their structure and provide a classification in small\ndimensions. We describe all possible pairs defining a Lie-Rinehart superalgebra\nfor $\\dim(A)\\leq 2$ and $\\dim(L)\\leq 4$. Moreover, we construct a cohomology\ncomplex and develop a theory of formal deformations based on formal power\nseries and this cohomology.","PeriodicalId":37836,"journal":{"name":"Communications in Mathematics","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2021-07-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On classification and deformations of Lie-Rinehart superalgebras\",\"authors\":\"Quentin Ehret, A. Makhlouf\",\"doi\":\"10.46298/cm.10537\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The purpose of this paper is to study Lie-Rinehart superalgebras over\\ncharacteristic zero fields, which are consisting of a supercommutative\\nassociative superalgebra $A$ and a Lie superalgebra $L$ that are compatible in\\na certain way. We discuss their structure and provide a classification in small\\ndimensions. We describe all possible pairs defining a Lie-Rinehart superalgebra\\nfor $\\\\dim(A)\\\\leq 2$ and $\\\\dim(L)\\\\leq 4$. Moreover, we construct a cohomology\\ncomplex and develop a theory of formal deformations based on formal power\\nseries and this cohomology.\",\"PeriodicalId\":37836,\"journal\":{\"name\":\"Communications in Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-07-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications in Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.46298/cm.10537\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46298/cm.10537","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Mathematics","Score":null,"Total":0}
On classification and deformations of Lie-Rinehart superalgebras
The purpose of this paper is to study Lie-Rinehart superalgebras over
characteristic zero fields, which are consisting of a supercommutative
associative superalgebra $A$ and a Lie superalgebra $L$ that are compatible in
a certain way. We discuss their structure and provide a classification in small
dimensions. We describe all possible pairs defining a Lie-Rinehart superalgebra
for $\dim(A)\leq 2$ and $\dim(L)\leq 4$. Moreover, we construct a cohomology
complex and develop a theory of formal deformations based on formal power
series and this cohomology.
期刊介绍:
Communications in Mathematics publishes research and survey papers in all areas of pure and applied mathematics. To be acceptable for publication, the paper must be significant, original and correct. High quality review papers of interest to a wide range of scientists in mathematics and its applications are equally welcome.