Connected cochain DG algebras of Calabi-Yau dimension 0
Connected cochain DG algebras of Calabi-Yau dimension 0
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DOI：
10.1090/proc/13081
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发表时间：
2016-11
期刊：
影响因子：
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通讯作者：
Ji-wei He;Xuefeng Mao
中科院分区：
文献类型：
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作者：
Ji-wei He;Xuefeng Mao
设一个连通的协链微分梯度代数（简称DG）。本文证明了a- calabi - yau DG代数当且仅当是Koszul DG代数，且$\ mathm {Tor} _A^ 0 (\Bbbk _A,{} _A\Bbbk) $是对称协代数。设一个有限维的向量空间和一个位势。则包含的最小子代数是一个对称的协代数，这意味着局部有限连通的协链DG代数是cy当且仅当它被一个势定义。参考文献
Letbe a connected cochain differential graded (DG, for short) algebra. This note shows thatis a-Calabi-Yau DG algebra if and only ifis a Koszul DG algebra and $\mathrm {Tor} _A^ 0 (\Bbbk _A,{} _A\Bbbk) $ is a symmetric coalgebra. Letbe a finite dimensional vector space anda potential in. Then the minimal subcoalgebra ofcontainingis a symmetric coalgebra, which implies that a locally finite connected cochain DG algebra is-CY if and only if it is defined by a potential. References