Geodesic
The $C^*$-algebra $\mathfrak{T}_m$ as a crossed product
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2014), pp. 24-30.

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In this paper we consider the $C^*$-subalgebra $\mathfrak{T}_m$ of the Toeplitz algebra $\mathfrak{T}$ generated by monomials, which have an index divisible by $m$. We present the algebra $\mathfrak{T}_m$ as a crossed product: $\mathfrak{T}_m=\varphi(A)\times_{\delta_m}\mathbb{Z}$, where $A=C_0 (\mathbb{Z}_+)\oplus\mathbb{C}I$ is $C^*$-algebra of all continuous functions on $\mathbb{Z}_+$, which have a finite limit at infinity. In the case $m=1$ we obtain that $\mathfrak{T}=\varphi(A)\times_{\delta_1}\mathbb{Z}$, which is an analogue of Coburn’s theorem.
Keywords: crossed product, finitely representable, Toeplitz algebra, $C^*$-algebra, transfer operator.
Mots-clés : index of monomial, coefficient algebra 
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K. H. Hovsepyan. The  $C^*$-algebra $\mathfrak{T}_m$ as a crossed product. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 3 (2014), pp. 24-30. http://geodesic.mathdoc.fr/item/UZERU_2014_3_a4/

[1] G.J. Murphy, “The Crossed Product of a $C^*$-Algebra by an Endomorphism”, Integral Equations Operator Theory, 24:3 (1996), 298–319 | DOI | MR | Zbl

[2] W.L. Paschke, “The Crossed Product of a $C^*$-Algebra by an Endomorphism”, Proc. Amer. Math. Soc., 80:1 (1980), 113–118 | MR | Zbl

[3] P.J. Stacey, “Crossed Products of $C^*$-Algebras by Endomorphisms”, J. Austral. Math. Soc. Ser. A, 54:2 (1993), 204–212 | DOI | MR | Zbl

[4] R. Exel, “A New Look at the Crossed-Product of a $C^*$-Algebra by an Endomorphism”, Ergodic Theory Dynam. Systems, 23:6 (2003), 1733–1750 | DOI | MR | Zbl

[5] A.V. Lebedev, A. Odzijewicz, “Extensions of $C^*$-Algebras by Partial Isometries”, Matem. Sbor., no. 195, 951–982 | MR | Zbl

[6] A.B. Antonevich, V.I. Bakhtin, A.V. Lebedev, “Crossed Product of a $C^*$-Algebra by an Endomorphism, Coefficient Algebras and Transfer Operators”, Matem. Sbor., 202 (2011), 1253–1283 | DOI | MR | Zbl

[7] M.A. Aukhadiev, S.A. Grigorian, E.V. Lipacheva, “Infinite-Dimensional Compact Quantum Semigroup”, Lobachevskii Journal of Mathematics, 2011, no. 4, 304–316 | MR | Zbl

[8] L.A. Coburn, “The $C^*$-Algebra Generated by an Isometry”, Bull. Amer. Math. Soc., 1967, no. 73, 722–726 | DOI | MR | Zbl