导括号与sh Leibniz代数
Derived brackets and sh Leibniz algebras
摘要：
我们开发了一个通用的框架，用于构建各种派生括号。我们表明，适当变形的微分分次莱布尼兹代数扩展派生括号建设，并导致强同伦（SH）莱布尼兹代数的概念。讨论了同伦代数理论、变形理论和导括号之间的联系。我们证明了派生的括号建设诱导适当定义的变形理论等价类的SH莱布尼兹代数的同构类的映射。
英文摘要：
We develop a general framework for the construction of various derived brackets. We show that suitably deforming the differential of a graded Leibniz algebra extends the derived bracket construction and leads to the notion of strong homotopy (sh) Leibniz algebra. We discuss the connections among homotopy algebra theory, deformation theory and derived brackets. We prove that the derived bracket construction induces a map from suitably defined deformation theory equivalence classes to the isomorphism classes of sh Leibniz algebras.
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