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Reference.org
Noncommutative torus
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, and more specifically in the theory of <a href="/facts/C*-algebra/B3tnGHIo">C*-algebras</a>, the noncommutative tori <i>A</i>θ, also known as irrational rotation algebras for <a href="/facts/Irrational_number/Psv19TET">irrational</a> values of θ, form a family of noncommutative C*-algebras which generalize the <a href="/facts/C*-algebra/B3tnGHIo">algebra of continuous functions</a> on the <a href="/facts/Torus/J9SkaV1W">2-torus</a>. 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 <a href="/facts/Noncommutative_geometry/WSwggL1p">noncommutative space</a> in the sense of <a href="/facts/Alain_Connes/tjFJ9Iou">Alain Connes</a>. </p>