Kabluchko, Z. A.; Proskurin, D. P.; Samojlenko, Yu. S. On \(C^*\)-algebras generated by deformations of the CCR. (Ukrainian, English) Zbl 1080.46047 Ukr. Mat. Zh. 56, No. 11, 1527-1538 (2004); translation in Ukr. Math. J. 56, No. 11, 1813-1827 (2004). The paper is devoted to \(C^*\)-algebras generated by a class of deformations of the canonical commutation relations (CCR) containing, in particular, the twisted CCR of W. Pusz and S. L. Woronowicz [Rep. Math. Phys. 27, No. 2, 231–257 (1989; Zbl 0707.47039)] and the commutation relations for generalized quons proposed by W. Marcinek [Rep. Math. Phys. 41, No. 2, 155–172 (1998; Zbl 0917.46069)].The authors show that the Fock representation is a universal bounded representation of the above \(C^*\)-algebra; in particular, it is faithful. Relations of this class of deformations with extensions of multi-dimensional noncommutative tori are discussed. Reviewer: A. N. Kochubei (Kyïv) MSC: 46L65 Quantizations, deformations for selfadjoint operator algebras Keywords:\(C^*\)-algebra; canonical commutation relations; Fock representation; noncommutative torus; generalized quons Citations:Zbl 0707.47039; Zbl 0917.46069 PDFBibTeX XMLCite \textit{Z. A. Kabluchko} et al., Ukr. Mat. Zh. 56, No. 11, 1527--1538 (2004; Zbl 1080.46047); translation in Ukr. Math. J. 56, No. 11, 1813--1827 (2004) Full Text: DOI