{"title":"非交换半群代数的第一和第二模上同调群","authors":"E. Nasrabadi","doi":"10.22130/SCMA.2020.119494.733","DOIUrl":null,"url":null,"abstract":"Let $S$ be a (not necessarily commutative) Clifford semigroup with idempotent set $E$. In this paper, we show that the first (second) Hochschild cohomology group and the first (second) module cohomology group of semigroup algbera $ell^1(S)$ with coefficients in $ell^infty(S)$ (and also $ell^1(S)^{(2n-1)}$ for $nin mathbb{N}$) are equal.","PeriodicalId":38924,"journal":{"name":"Communications in Mathematical Analysis","volume":"17 1","pages":"39-47"},"PeriodicalIF":0.0000,"publicationDate":"2020-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"First and Second Module Cohomology Groups for Non Commutative Semigroup Algebras\",\"authors\":\"E. Nasrabadi\",\"doi\":\"10.22130/SCMA.2020.119494.733\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let $S$ be a (not necessarily commutative) Clifford semigroup with idempotent set $E$. In this paper, we show that the first (second) Hochschild cohomology group and the first (second) module cohomology group of semigroup algbera $ell^1(S)$ with coefficients in $ell^infty(S)$ (and also $ell^1(S)^{(2n-1)}$ for $nin mathbb{N}$) are equal.\",\"PeriodicalId\":38924,\"journal\":{\"name\":\"Communications in Mathematical Analysis\",\"volume\":\"17 1\",\"pages\":\"39-47\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-11-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications in Mathematical Analysis\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22130/SCMA.2020.119494.733\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Mathematical Analysis","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22130/SCMA.2020.119494.733","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"Mathematics","Score":null,"Total":0}
First and Second Module Cohomology Groups for Non Commutative Semigroup Algebras
Let $S$ be a (not necessarily commutative) Clifford semigroup with idempotent set $E$. In this paper, we show that the first (second) Hochschild cohomology group and the first (second) module cohomology group of semigroup algbera $ell^1(S)$ with coefficients in $ell^infty(S)$ (and also $ell^1(S)^{(2n-1)}$ for $nin mathbb{N}$) are equal.
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