Leibniz algebras with derivations

IF 0.5 4区数学 Journal of Homotopy and Related Structures Pub Date : 2021-04-09 DOI:10.1007/s40062-021-00280-w

Apurba Das

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.

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带导数的莱布尼兹代数

在本文中，我们考虑带导数的莱布尼兹代数。由一个莱布尼茨代数和一个特殊的导数组成的一对称为莱布德对。我们定义了带系数的LeibDer对的上同调理论。我们研究了LeibDer对的中心扩展。在接下来，我们将形式变形理论推广到LeibDer对，其中我们变形了Leibniz括号和微分导数。它是由本身有系数的LeibDer对的上同调支配的。最后，我们考虑了Leibniz代数上的同伦导和Leibniz代数上的2导。具有同伦导数的2项h -莱布尼兹代数的范畴等价于具有2导的2-莱布尼兹代数的范畴。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Homotopy and Related Structures Mathematics-Geometry and Topology

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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.

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