M. A. Aukhadiev, A. S. Nikitin, A. S. Sitdikov, “Crossed product of the canonical anticommutative relations algebra in the Cuntz algebra”, Izv. Vyssh. Uchebn. Zaved. Mat., 2014, Number 8,Pages <nobr>86

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Brief communications

Crossed product of the canonical anticommutative relations algebra in the Cuntz algebra

M. A. Aukhadiev, A. S. Nikitin, A. S. Sitdikov

Chair of Higher Mathematics, Kazan State Power Engineering University, 51 Krasnosel'skaya str., Kazan, 420066 Russia

Abstract: We show that the Cuntz algebra is a $C^*$-crossed product of the canonical anticommutation relations algebra, generated by a standard recursive fermion system, with the group of integers by endomorphism.

Keywords: Cuntz algebra, crossed product, recursive fermion system, algebra of fields, $C^*$-algebra, isometry.

UDC: 512.667+517.518

Presented by the member of Editorial Board: A. M. Bikchentaev
Received: 24.03.2014