Representation Stacks, D-Branes and Noncommutative Geometry

Abstract

In this note we prove that the -points of the representation Artin-stack of n-dimensional representations of an affine ℂ-algebra R correspond to ℂ-algebra morphisms R → A _n where A _n is an Azumaya algebra of degree n over C. We connect this to the theory of D-branes and Azumaya noncommutative geometry, developed by Chien-Hao Liu and Shing-Tung Yau in a series of articles [9]–[14].

Key Words:

• D-branes
• Representation schemes
• Stacks

2000 Mathematics Subject Classification:

• Primary 14A20
• Secondary 16R30
• 14A22

Notes

Communicated by L. Small.