摘要翻译:
本文证明了上同调内积不变的强同伦交换(或$C_\infty$-)代数可唯一推广为辛$C_\infty$-代数(由Kontsevich引入的交换Frobenius代数的$\infty$-推广)。这一结果依赖于$\ci$-代数的循环Hochschild上同调的代数Hodge分解,不能推广到其他运算域上的代数。
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英文标题:
《Symplectic $C_\infty$-algebras》
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作者:
Alastair Hamilton and Andrey Lazarev
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最新提交年份:
2007
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分类信息:
一级分类:Mathematics 数学
二级分类:Quantum Algebra 量子代数
分类描述:Quantum groups, skein theories, operadic and diagrammatic algebra, quantum field theory
量子群,skein理论,运算代数和图解代数,量子场论
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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:K-Theory and Homology K-理论与同调
分类描述:Algebraic and topological K-theory, relations with topology, commutative algebra, and operator algebras
代数和拓扑K-理论,与拓扑的关系,交换代数和算子代数
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英文摘要:
In this paper we show that a strongly homotopy commutative (or $C_\infty$-) algebra with an invariant inner product on its cohomology can be uniquely extended to a symplectic $C_\infty$-algebra (an $\infty$-generalisation of a commutative Frobenius algebra introduced by Kontsevich). This result relies on the algebraic Hodge decomposition of the cyclic Hochschild cohomology of a $\ci$-algebra and does not generalize to algebras over other operads.
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PDF链接:
https://arxiv.org/pdf/0707.3951