Representation Stacks, D-Branes and Noncommutative Geometry

摘要

In this note we prove that the -points of the representation Artin-stack of n-dimensional representations of an affine ?-algebra R correspond to ?-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].