Calabi-Yau Frobenius algebras
Calabi-Yau Frobenius algebras
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DOI：
10.1016/j.jalgebra.2008.11.003
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发表时间：
2007-10
期刊：
影响因子：
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通讯作者：
C. Eu;T. Schedler
中科院分区：
文献类型：
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作者：
C. Eu;T. Schedler
我们定义了任意基交换环上的Calabi-Yau Frobenius代数。我们定义了Tate上同调的Hochschild类似，并证明了周期CY Frobenius代数的这种“稳定的Hochschild上同调”具有Batalin-Vilkovisky和Frobenius代数结构。此类代数包括(广义)dykin箭图的(中心扩张的)预投射代数和经典周期群的群代数。我们首次利用这个理论计算了许多与箭图有关的代数的Hochschild上同调，从而简化了已有结果的描述。此外，我们还计算了从扩展的动态预射射代数到动态预射射代数的上同调映射，从而将我们的CY性质(对于Frobenius代数)和Ginzburg性质(对于有限Hochschild维代数)联系起来。
We define Calabi–Yau Frobenius algebras over arbitrary base commutative rings. We define a Hochschild analogue of Tate cohomology, and show that this “stable Hochschild cohomology” of periodic CY Frobenius algebras has a Batalin–Vilkovisky and Frobenius algebra structure. Such algebras include (centrally extended) preprojective algebras of (generalized) Dynkin quivers, and group algebras of classical periodic groups. We use this theory to compute (for the first time) the Hochschild cohomology of many algebras related to quivers, and to simplify the description of known results. Furthermore, we compute the maps on cohomology from extended Dynkin preprojective algebras to the Dynkin ones, which relates our CY property (for Frobenius algebras) to that of Ginzburg (for algebras of finite Hochschild dimension).