Aukhadiev, M. A.; Nikitin, A. S.; Sitdikov, A. S. A crossed product of the canonical anticommutation relations algebra in the Cuntz algebra. (English. Russian original) Zbl 1315.46055 Russ. Math. 58, No. 8, 71-73 (2014); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2014, No. 8, 86-89 (2014). Summary: We show that the Cuntz algebra can be represented as a crossed product of the canonical anticommutation relations algebra by an endomorphism. Cited in 1 Document MSC: 46L05 General theory of \(C^*\)-algebras 46L55 Noncommutative dynamical systems Keywords:Cuntz algebra; crossed product; recursive fermion system; \(C^*\)-algebra; isometry PDFBibTeX XMLCite \textit{M. A. Aukhadiev} et al., Russ. Math. 58, No. 8, 71--73 (2014; Zbl 1315.46055); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 2014, No. 8, 86--89 (2014) Full Text: DOI References: [1] Doplicher, S., Roberts, J.E. “Why there is a Field Algebra with a Compact Gauge Group Describing The Superselection Structure in Particle Physics,” Comm. Math. Phys. 131, 51-107 (1990). · Zbl 0734.46042 · doi:10.1007/BF02097680 [2] Doplicher, S., Roberts, J. E. “Endomorphisms of <Emphasis Type=”Italic“>C*-Algebras,” Ann. Math. 130, 75-119 (1989). · Zbl 0702.46044 · doi:10.2307/1971477 [3] Doplicher, S., Roberts, J. E. “ANew Duality Theory for CompactGroups,” Invent. Math. 98, 157-218 (1989). · Zbl 0691.22002 · doi:10.1007/BF01388849 [4] Doplicher, S., Haag, R., Roberts, J. E. “Local Observables and Particle Statistics. I,” Comm. Math Phys. 23, 199-230 (1971); “Local Observables and Particle Statistics. II,” Comm. Math. Phys. 35, 49-85 (1974). · doi:10.1007/BF01877742 [5] Antonevich, A. B., Bakhtin, V. I., Lebedev, A. V. “Crossed Product of a <Emphasis Type=”Italic“>C*-Algebra by an Endomorphism, Coefficient Algebras and Transfer Operators,” Sb. Math. 202, No. 9-10, 1253-1283 (2011). · Zbl 1242.46074 · doi:10.1070/SM2011v202n09ABEH004186 [6] Abe, M., Kawamura, K. “Recursive Fermion System in Cuntz Algebra. I. Embeddings of Fermion Algebra into Cuntz Algebra,” Comm. Math. Phys. 228, 85-101 (2002). · Zbl 1029.46079 · doi:10.1007/s002200200651 [7] Bratteli, O., Robinson, D. Operator Algebras and Quantum Statistical Mechanics (Springer, 2003), Vol. I. · Zbl 0463.46052 [8] Lebedev, A.V., Odzijewicz, A. Extensions of C*-algebras by Partial Isometries, Sb. Math. 195, 951-982 (2004). · Zbl 1081.46037 · doi:10.1070/SM2004v195n07ABEH000834 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.