论文标题
Hochschild的限制谎言代数结构的稳定不变性
Stable invariance of the restricted Lie algebra structure of Hochschild cohomology
论文作者
论文摘要
我们表明，在自注射代数之间的莫里塔类型的稳定等效性下，霍基柴尔德共同体的限制性代数结构是不变的。因此，我们获得了许多积极的特征稳定不变性，例如$ p $ - 级等级为$ \ mathrm {hh}^1（a，a，a）$。我们还证明了关于iwanaga-gorenstein代数的更一般的结果，使用了莫里塔类型的稳定等效概念。在交换代数和模块化表示理论中提供了几种应用。首先建立了Hochschild Cochain Complex的$ B_ \ Infty $ - 结构的稳定不变性，从而证明了这些结果。在附录中，我们解释了如何将Hochschild同谋的$ P $ - 功率操作视为该$ B_ \ Infty $ - 结构的工件。特别是，我们使用Operad的语言建立了$ p $ - 功率操作的明确定义 - 最初是拓扑 - Cohen和Turchin引起的方法。
We show that the restricted Lie algebra structure on Hochschild cohomology is invariant under stable equivalences of Morita type between self-injective algebras. Thereby we obtain a number of positive characteristic stable invariants, such as the $p$-toral rank of $\mathrm{HH}^1(A,A)$. We also prove a more general result concerning Iwanaga-Gorenstein algebras, using a more general notion of stable equivalences of Morita type. Several applications are given to commutative algebra and modular representation theory. These results are proven by first establishing the stable invariance of the $B_\infty$-structure of the Hochschild cochain complex. In the appendix we explain how the $p$-power operation on Hochschild cohomology can be seen as an artifact of this $B_\infty$-structure. In particular, we establish well-definedness of the $p$-power operation, following some -- originally topological -- methods due to May, Cohen and Turchin, using the language of operads.
