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Calabi-Yau categories and graded quivers with potential

Jie Ren

Abstract

We prove that the equivalence classes of d-dimensional Calabi-Yau $A_\infty$-categories (dCY category for short) of certain type are in one-to-one correspondence with the gauge equivalence classes of graded quivers with potential.

Calabi-Yau categories and graded quivers with potential

Abstract

We prove that the equivalence classes of d-dimensional Calabi-Yau -categories (dCY category for short) of certain type are in one-to-one correspondence with the gauge equivalence classes of graded quivers with potential.
Paper Structure (3 sections, 1 theorem, 5 equations)

This paper contains 3 sections, 1 theorem, 5 equations.

Table of Contents

  1. Introduction
  2. d Calabi-Yau categories
  3. Main theorem

Key Result

Theorem 3.1

Let ${\mathscr C}$ be a d-dimensional k-linear Calabi-Yau category generated by a finite collection ${\mathcal{E}}=\{E_{i}\}_{i\in I}$ of generators satisfying The equivalence classes of such categories with respect to $A_{\infty}$-transformations preserving the Calabi-Yau structure and $\mathcal{E}$, are in one-to-one correspondence with the gauge equivalence classes of pairs $(\overline Q,W)$.

Theorems & Definitions (6)

  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • Definition 2.4
  • Theorem 3.1
  • proof