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math.QA2007
Heisenberg modules over real multiplication noncommutative tori and related algebraic structures
Jorge Plazas
We review some aspects of the theory of noncommutative two-tori with real multiplication focusing on the role played by Heisenberg groups in the definition of algebraic structures…
math.QA2007
Examples of noncommutative manifolds: complex tori and spherical manifolds
Jorge Plazas
We survey some aspects of the theory of noncommutative manifolds focusing on the noncommutative analogs of two-dimensional tori and low-dimensional spheres. We are particularly int…
math.NT2007
Quantum statistical mechanics and class field Theory
Jorge Plazas
We survey some results relating noncommutative geometry to the class field theory of number fields. These results appear within the context of quantum statistical mechanics where s…