Hochschild cohomology of Fermat type polynomials with non–abelian symmetries

Abstract

For a polynomial f=x1n+…+xNn let Gf be the non–abelian maximal group of symmetries of f. This is a group generated by all g∈GL(N,C), rescaling and permuting the variables, so that f(x)=f(g⋅x). For any G⊆Gf we compute explicitly Hochschild cohomology of the category of G–equivariant matrix factorizations of f. We introduce the pairing on it showing that it is a Frobenius algebra.