THE $ C^*$-ALGEBRA $\mathcal{T}_m$ AS A CROSSED PRODUCT

Authors

  • K.H. Hovsepyan Kazan State Power Engineering University, Russian Federation

DOI:

https://doi.org/10.46991/PSYU:A/2014.48.3.024

Keywords:

index of monomial, coefficient algebra, crossed product, finitely representable, Toeplitz algebra, $C^*$-algebra, transfer operator

Abstract

In this paper we consider the $ C^*$-subalgebra $\mathcal{T}_m$ of the Toeplitz algebra  $\mathcal{T}$ generated by monomials, which have an index divisible by $m$. We present the algebra $\mathcal{T}_m$ as a crossed product: $\mathcal{T}_m=\varphi(\mathcal{A})\times_{\delta_m}\mathbb{Z}$, where $\mathcal{A}=C_0(\mathbb{Z}_+)\oplus \mathbb{C}I$ 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 $\mathcal{T}=\varphi(\mathcal{A})\times_{\delta_1}\mathbb{Z}$, which is an analogue of Coburn's theorem.

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Published

2014-11-03

How to Cite

Hovsepyan, K. (2014). THE $ C^*$-ALGEBRA $\mathcal{T}_m$ AS A CROSSED PRODUCT. Proceedings of the YSU A: Physical and Mathematical Sciences, 48(3 (235), 24–30. https://doi.org/10.46991/PSYU:A/2014.48.3.024

Issue

Section

Mathematics