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Noncommutative balls and their doubles. (English) Zbl 1109.46060

Summary: Quantum analogues of \(n\)-dimensional balls are defined via suitable generators and relations. In the even case, they correspond to the twisted canonical commutation relations of Pusz and Woronowicz. Then we construct quantum spheres as double manifolds of the noncommutative balls.

MSC:

46L89 Other “noncommutative” mathematics based on \(C^*\)-algebra theory
58B34 Noncommutative geometry (à la Connes)
81R60 Noncommutative geometry in quantum theory
81R15 Operator algebra methods applied to problems in quantum theory
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