{"title":"Leibniz algebras with derivations","authors":"Apurba Das","doi":"10.1007/s40062-021-00280-w","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we consider Leibniz algebras with derivations. A pair consisting of a Leibniz algebra and a distinguished derivation is called a LeibDer pair. We define a cohomology theory for LeibDer pair with coefficients in a representation. We study central extensions of a LeibDer pair. In the next, we generalize the formal deformation theory to LeibDer pairs in which we deform both the Leibniz bracket and the distinguished derivation. It is governed by the cohomology of LeibDer pair with coefficients in itself. Finally, we consider homotopy derivations on sh Leibniz algebras and 2-derivations on Leibniz 2-algebras. The category of 2-term sh Leibniz algebras with homotopy derivations is equivalent to the category of Leibniz 2-algebras with 2-derivations.</p>","PeriodicalId":636,"journal":{"name":"Journal of Homotopy and Related Structures","volume":"16 2","pages":"245 - 274"},"PeriodicalIF":0.5000,"publicationDate":"2021-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1007/s40062-021-00280-w","citationCount":"20","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Homotopy and Related Structures","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s40062-021-00280-w","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 20
Abstract
In this paper, we consider Leibniz algebras with derivations. A pair consisting of a Leibniz algebra and a distinguished derivation is called a LeibDer pair. We define a cohomology theory for LeibDer pair with coefficients in a representation. We study central extensions of a LeibDer pair. In the next, we generalize the formal deformation theory to LeibDer pairs in which we deform both the Leibniz bracket and the distinguished derivation. It is governed by the cohomology of LeibDer pair with coefficients in itself. Finally, we consider homotopy derivations on sh Leibniz algebras and 2-derivations on Leibniz 2-algebras. The category of 2-term sh Leibniz algebras with homotopy derivations is equivalent to the category of Leibniz 2-algebras with 2-derivations.
期刊介绍：
Journal of Homotopy and Related Structures (JHRS) is a fully refereed international journal dealing with homotopy and related structures of mathematical and physical sciences.
Journal of Homotopy and Related Structures is intended to publish papers on
Homotopy in the broad sense and its related areas like Homological and homotopical algebra, K-theory, topology of manifolds, geometric and categorical structures, homology theories, topological groups and algebras, stable homotopy theory, group actions, algebraic varieties, category theory, cobordism theory, controlled topology, noncommutative geometry, motivic cohomology, differential topology, algebraic geometry.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
