{"title":"约旦上代数和相关列上代数的循环同源性","authors":"Consuelo Martínez, Efim Zelmanov, Zezhou Zhang","doi":"arxiv-2409.03726","DOIUrl":null,"url":null,"abstract":"We study the relationship between cyclic homology of Jordan superalgebras and\nsecond cohomologies of their Tits-Kantor-Koecher Lie superalgebras. In particular, we focus on Jordan superalgebras that are Kantor doubles of\nbracket algebras. The obtained results are applied to computation of second\ncohomologies and universal central extensions of Hamiltonian and contact type\nLie superalgebras over arbitrary rings of coefficients.","PeriodicalId":501136,"journal":{"name":"arXiv - MATH - Rings and Algebras","volume":"41 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Cyclic homology of Jordan superalgebras and related Lie superalgebras\",\"authors\":\"Consuelo Martínez, Efim Zelmanov, Zezhou Zhang\",\"doi\":\"arxiv-2409.03726\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We study the relationship between cyclic homology of Jordan superalgebras and\\nsecond cohomologies of their Tits-Kantor-Koecher Lie superalgebras. In particular, we focus on Jordan superalgebras that are Kantor doubles of\\nbracket algebras. The obtained results are applied to computation of second\\ncohomologies and universal central extensions of Hamiltonian and contact type\\nLie superalgebras over arbitrary rings of coefficients.\",\"PeriodicalId\":501136,\"journal\":{\"name\":\"arXiv - MATH - Rings and Algebras\",\"volume\":\"41 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Rings and Algebras\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.03726\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Rings and Algebras","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.03726","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Cyclic homology of Jordan superalgebras and related Lie superalgebras
We study the relationship between cyclic homology of Jordan superalgebras and
second cohomologies of their Tits-Kantor-Koecher Lie superalgebras. In particular, we focus on Jordan superalgebras that are Kantor doubles of
bracket algebras. The obtained results are applied to computation of second
cohomologies and universal central extensions of Hamiltonian and contact type
Lie superalgebras over arbitrary rings of coefficients.