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Journal of the London Mathematical Society Advance Access originally published online on March 3, 2008
Journal of the London Mathematical Society 2008 77(3):607-626; doi:10.1112/jlms/jdn003
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© 2008 London Mathematical Society

Noncommutative balls and mirror quantum spheres

Jeong Hee Hong

Department of Mathematics
The University of Newcastle
Newcastle, NSW 2308
Australia
Current address:
Applied Mathematics
Korea Maritime University
Busan 606–791
South Korea

Wojciech Szymanski

Department of Mathematics
The University of Newcastle
Newcastle, NSW 2308
Australia
Wojciech.Szymanski@newcastle.edu.au

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 analysed, 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’.

2000 Mathematics Subject Classification 46L65, 46L80.

The first author is supported by the Korea Research Foundation Grant (KRF-2004-041-C00024). The second author is partially supported by the KBN grant 1 P03A 036 26, the European Commission grant MKTD-CT-2004-509794, and the ARC Linkage International Fellowship LX0667294.

Received May 16, 2007; revised August 23, 2007; published online March 3, 2008.


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