Matrix Factorizations and Representations of Quivers II: type ADE case

TL;DR

This paper explores the relationship between graded matrix factorizations of ADE-type polynomials and derived categories of Dynkin quivers, establishing an equivalence and analyzing stability conditions.

Contribution

It demonstrates an equivalence between a triangulated category of matrix factorizations and the derived category of Dynkin quiver modules, and discusses stability conditions defined by grading.

Findings

Equivalence between matrix factorizations and derived categories of Dynkin quivers

Identification of a natural stability condition from grading

Insights into the structure of triangulated categories for ADE polynomials

Abstract

We study a triangulated category of graded matrix factorizations for a polynomial of type ADE. We show that it is equivalent to the derived category of finitely generated modules over the path algebra of the corresponding Dynkin quiver. Also, we discuss a special stability condition for the triangulated category in the sense of T. Bridgeland, which is naturally defined by the grading.