Matrix Factorizations and Representations of Quivers I

2005/06/17 by Atsushi Takahashi, Takahashi, Atsushi · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.math/0506347

20 pages, added references

arxiv created 2005/09/21 · arxiv updated 2009/12/01

Abstract

This paper introduces a mathematical definition of the category of D-branes in Landau-Ginzburg orbifolds in terms of A_∞-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 xⁿ⁺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.

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