Matrix Factorizations and Representations of Quivers I

Abstract

This paper introduces a mathematical definition of the category of D-branes in Landau-Ginzburg orbifolds in terms of $A_{\infty }$-categories. Our categories coincide with the categories of (graded) matrix factorizations for quasi-homogeneous polynomials. After setting up the necessary definitions, we prove that our category for the polynomial $x^{n+1}$ is equivalent to the derived category of representations of the Dynkin quiver of type $A_n$. We also construct a special stability condition for the triangulated category in the sense of T. Bridgeland, which should be the "origin" of the space of stability conditions.

20 pages, added references

Cited by in corpus (1)

• A Remark on a Theorem of math.AG/0511155