On orbifold Jacobian algebras for invertible polynomials
Motivated by some algebraic structures on the pair of Hochshild cohomology and homology groups, we propose an axiom for the ``orbifold Jacobian algebra", the Jacobian algebra for a pair of isolated hypersurface singularity and a finite group preserving the defining polynomial of the singularity, in physics terminology, the B-model chiral algebra for Landau-Ginzburg orbifolds. We show the existence and the uniqueness of the orbifold Jacobian algebra for an invertible polynomial and its symmetry group. The relation to the category of equivariant matrix factorizations will also be given. This is a joint work with Alexey Basalaev and Elisabeth Werner.