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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.

MSC:

46L65 Quantizations, deformations for selfadjoint operator algebras
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