# Hochschild cohomology and orbifold Jacobian algebras associated to invertible polynomials

### Alexey Basalaev

Skolkovo Institute of Science and Technology, Moscow, Russia, and University of Heidelberg, Germany### Atsushi Takahashi

Osaka University, Japan

## Abstract

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 $Z/2ZZ$-graded algebra to the Hochschild cohomology $HH_{∗}(MF_{G}(f))$ of the dg-category $MF_{G}(f)$ of $G$-equivariant matrix factorizations of $f$ by calculating the product formula of $HH_{∗}(MF_{G}(f))$ given by Shklyarov [10]. We also discuss the relation of our previous results to the categorical equivalence.

## Cite this article

Alexey Basalaev, Atsushi Takahashi, Hochschild cohomology and orbifold Jacobian algebras associated to invertible polynomials. J. Noncommut. Geom. 14 (2020), no. 3, pp. 861–877

DOI 10.4171/JNCG/370