Hochschild cohomology and orbifold Jacobian algebras associated to invertible polynomials
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 [BTW16] is isomorphic as a Z/2Z-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 [S17]. We also
discuss the relation of our previous results to the categorical equivalence.