High Quality Content by WIKIPEDIA articles! A quantum torus is a "space" whose noncommutative algebra of functions is obtained by deformation of the commutative algebra of functions on a torus (R/Z)d. It is a noncommutative analogue of the algebra of Laurent polynomials. Quantum tori appear in extended affine Lie algebra and quantum physics. In noncommutative geometry or quantum physics, a noncommutative torus is a special type of quantum torus. In the 1980s and 1990s Alain Connes introduced a range of new geometric objects designed to put quantum physics on a firm mathematical foundation. One of the most important examples was the quantum torus, an abstract, quantum version of the traditional doughnut-shaped torus. While a classical torus is easy to visualise, it is impossible to picture a quantum torus in the same way.

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