Noncommutative torus

• abstract: In mathematics, and more specifically in the theory of C*-algebras, the noncommutative tori Aθ (also known as irrational rotation algebras when θ is irrational) are a family of noncommutative C*-algebras which generalize the algebra of continuous functions on the 2-torus. Many topological and geometric properties of the classical 2-torus have algebraic analogues for the noncommutative tori, and as such they are fundamental examples of a noncommutative space in the sense of Alain Connes.

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