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arXiv · 1009.5203

Representation stacks, D-branes and noncommutative geometry

Lieven Le Bruyn
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Abstract

In this note we prove that the spec(C)-points of the representation Artin-stack [rep_n R/PGL_n] of n-dimensional representations of an affine algebra R correspond to algebra morphisms R-->A where A is an Azumaya algebra of degree n over C. We connect this to the study of D-branes and Azumaya noncommutative geometry, developed by Chien-Hao Liu and Shing-Tung Yau in a series of papers from arXiv:0709.1515 to arXiv:1003.1178

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Lieven Le Bruyn. 2010-09-27. Representation stacks, D-branes and noncommutative geometry. https://arxiv.org/abs/1009.5203

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