Fundamental matrix factorization in the FJRW-theory revisited

TL;DR

This paper improves the construction of the fundamental matrix factorization in FJRW-theory, making it coordinate-free and applicable to nonabelian symmetry groups, using dg-matrix factorizations over dg-schemes.

Contribution

It introduces a coordinate-free construction of the fundamental matrix factorization in FJRW-theory that works for nonabelian symmetry groups.

Findings

Coordinate-free construction of the fundamental matrix factorization

Extension to nonabelian finite groups of symmetries

Use of dg-matrix factorizations over dg-schemes

Abstract

We present an improved construction of the fundamental matrix factorization in the FJRW-theory given in arXiv:1105.2903. The revised construction is coordinate-free and works for a possibly nonabelian finite group of symmetries. One of the new ingrediants is the category of dg-matrix factorizations over a dg-scheme.