Hong, Jeong Hee; Szymański, Wojciech Noncommutative balls and their doubles. (English) Zbl 1109.46060 Czech. J. Phys. 56, No. 10-11, 1173-1178 (2006). 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. Cited in 2 Documents 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 Keywords:noncommutative ball; quantum sphere; \(C^*\)-algebra PDFBibTeX XMLCite \textit{J. H. Hong} and \textit{W. Szymański}, Czech. J. Phys. 56, No. 10--11, 1173--1178 (2006; Zbl 1109.46060) Full Text: DOI References: [1] W. Pusz and S.L. Woronowicz: Rep. Math. Phys.27 (1989) 231. · Zbl 0707.47039 · doi:10.1016/0034-4877(89)90006-2 [2] A.J.-L. Sheu: Commun. Math. Phys.135 (1991) 217. · Zbl 0719.58042 · doi:10.1007/BF02098041 [3] P.M. Hajac, R. Matthes, and W. Szymański: math.KT/0511309. [4] L.L. Vaksman and Y.S. Soibelman: Algebra i Analiz2 (1990) 101. [5] S.L. Woronowicz: Publ. Res. Inst. Math. Sci.23 (1987) 117. · Zbl 0676.46050 · doi:10.2977/prims/1195176848 [6] J.H. Hong and W. Szymański: Commun. Math. Phys.232 (2002) 157. · Zbl 1015.81029 · doi:10.1007/s00220-002-0732-1 [7] L. Faddeev, N. Reshetikhin, and L. Takhtajan: Leningrad. Math. J.1 (1990) 193. [8] E. Hawkins and G. Landi: J. Geom. Phys.49 (2004) 272. · Zbl 1065.19002 · doi:10.1016/S0393-0440(03)00092-5 [9] P. Podleś: Lett. Math. Phys.14 (1987) 193. · Zbl 0634.46054 · doi:10.1007/BF00416848 [10] P. Baum, P.M. Hajac, R. Matthes, and W. Szymański:K-theory, to appear. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.