Let $f$ be an invertible polynomial and $G$ a group of diagonal symmetries of $f$. This note shows that the orbifold Jacobian algebra $\mathrm{ Jac}(f,G)$ of $(f,G)$ defined by the authors and Elisabeth Werner in arXiv:1608.08962 is isomorphic as a $\mathbb{ ZZ}/2\mathbb{ ZZ}$-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 in arXiv:1708.06030. We also discuss the relation of our previous results to the categorical equivalence.
Categories: math.AG