From Large N Matrices to the Noncommutative Torus

1999/12/15 by G. Landi, F. Lizzi, R. J. Szabo · 3 citations
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #Noncommutative and Quantum Gravity Theories #cond-mat #gr-qc #hep-lat #hep-th #math-ph #math.MP #math.QA

paper · pdf · doi:10.1007/s002200000356

published as Commun.Math.Phys. 217 (2001) 181-201 · 23 pages LaTeX2e

arxiv created 1999/12/15 · arxiv updated 2009/11/30

Abstract

We describe how and to what extent the noncommutative two-torus can be approximated by a tower of finite-dimensional matrix geometries. The approximation is carried out for both irrational and rational deformation parameters by embedding the algebra of the noncommutative torus into an approximately finite algebra. The construction is a rigorous derivation of the recent discretizations of noncommutative gauge theories using finite dimensional matrix models, and it shows precisely how the continuum limits of these models must be taken. We clarify various aspects of Morita equivalence using this formalism and describe some applications to noncommutative Yang-Mills theory.

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