Let $f$ be an invertible polynomial and $G$ a group of diagonal symmetries of $f$. This note shows that the orbifold Jacobian algebra Jac$(f,G)$ of $(f,G)$ defined by [2] is isomorphic as a $\mathbb Z/2\mathbb ZZ$-graded algebra to the Hochschild cohomology $\mathsf{HH}^*(\mathrm {MF}_G(f))$ of the dg-category $\mathrm {MF}_G(f)$ of $G$-equivariant matrix factorizations of $f$ by calculating the product formula of $\mathsf{HH}^*(\mathrm {MF}_G(f))$ given by Shklyarov [10]. We also discuss the relation of our previous results to the categorical equivalence.

中文翻译：

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与可逆多项式相关的Hochschild同调和单Jacobian代数

假设$ f $是可逆多项式，而$ G $是一组对角对称$ f $。该注释表明，[2]定义的$（f，G）$的雅可比雅可比代数Jac $（f，G）$同构为Hochschild同调的$ \ mathbb Z / 2 \ mathbb ZZ $阶代数。 dg类的$ \ mathsf {HH} ^ *（\ mathrm {MF} _G（f））$ $ G $的$ \ mathrm {MF} _G（f）$-等价矩阵分解为$ f $ Shklyarov [10]给出的$ \ mathsf {HH} ^ *（\ mathrm {MF} _G（f））$的乘积公式。我们还讨论了先前结果与绝对等价关系。