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Mathematics > Operator Algebras

arXiv:math/0701799 (math)
[Submitted on 28 Jan 2007 (v1), last revised 4 Aug 2007 (this version, v2)]

Title:Noncommutative Balls and Mirror Quantum Spheres

Authors:Jeong Hee Hong, Wojciech Szymanski
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Abstract: Noncommutative analogues of n-dimensional balls are defined by repeated application of the quantum double suspension to the classical low-dimensional spaces. In the `even-dimensional' case they correspond to the Twisted Canonical Commutation Relations of Pusz and Woronowicz. Then quantum spheres are constructed as double manifolds of noncommutative balls. Both C*-algebras and polynomial algebras of the objects in question are defined and analyzed, and their relations with previously known examples are presented. Our construction generalizes that of Hajac, Matthes and Szymanski for `dimension 2', and leads to a new class of quantum spheres (already on the C*-algebra level) in all `even-dimensions'.
Comments: 20 pages
Subjects: Operator Algebras (math.OA); Quantum Algebra (math.QA)
MSC classes: 46L65, 46L87
Cite as: arXiv:math/0701799 [math.OA]
  (or arXiv:math/0701799v2 [math.OA] for this version)
  https://doi.org/10.48550/arXiv.math/0701799
Related DOI: https://doi.org/10.1112/jlms/jdn003

Submission history

From: Jeong Hee Hong Ph.D [view email]
[v1] Sun, 28 Jan 2007 01:55:39 UTC (20 KB)
[v2] Sat, 4 Aug 2007 07:32:08 UTC (20 KB)
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