摘要翻译：
设R是包含有理子环的交换环，设g是链复形。假定给定g上的一个sh-Lie代数结构，即余自由余增微分次余交换余代数T′上的余代数微分在g的悬置上的一个余代数摄动，并将摄动余代数写成T“。假设，此外，给出了g在链复形M上的压缩，我们证明了该数据确定了M上的一个sh-Lie代数结构，即在M的悬置上的余自由余增微分次可交换余代数S'上的余代数微分的一个余代数扰动，在扰动余代数T上的李代数扭余链到循环李代数L,以及该李代数扭余链到L上的Cartan-Chevalley-Eilenberg余代数上的链复形压缩的一个推广，这在数据中是自然的。对于M和g连通的特殊情况，我们还构造了摄动缩回的显式扩张到sh-Lie映射。这种方法包括主方程的一个非常一般的解。
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英文标题：
《The sh-Lie algebra perturbation Lemma》
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作者：
Johannes Huebschmann (Universite de Lille 1)
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最新提交年份：
2010
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分类信息：

一级分类：Mathematics        数学
二级分类：Algebraic Geometry        代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics        数学
二级分类：Commutative Algebra        交换代数
分类描述：Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics
交换环，模，理想，同调代数，计算方面，不变理论，与代数几何和组合学的联系
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英文摘要：
  Let R be a commutative ring which contains the rationals as a subring and let g be a chain complex. Suppose given an sh-Lie algebra structure on g, that is, a coalgebra perturbation of the coalgebra differential on the cofree coaugmented differential graded cocommutative coalgebra T' on the suspension of g and write the perturbed coalgebra as T". Suppose, furthermore, given a contraction of g onto a chain complex M. We show that the data determine an sh-Lie algebra structure on M, that is, a coalgebra perturbation of the coalgebra differential on the cofree coaugmented differential graded cocommutative coalgebra S' on the suspension of M, a Lie algebra twisting cochain from the perturbed coalgebra S" to the loop Lie algebra L on the perturbed coalgebra T", and an extension of this Lie algebra twisting cochain to a contraction of chain complexes from the Cartan-Chevalley-Eilenberg coalgebra on L onto S" which is natural in the data. For the special case where M and g are connected we also construct an explicit extension of the perturbed retraction to an sh-Lie map. This approach includes a very general solution of the master equation.
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PDF链接：
https://arxiv.org/pdf/0710.2070