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Proceedings of the YSU, Physical and Mathematial Scineces, 2014, Issue 3, Pages 24–30 (Mi uzeru68)  

This article is cited in 2 scientific papers (total in 2 papers)

Mathematics

The $C^*$-algebra $\mathfrak{T}_m$ as a crossed product

K. H. Hovsepyan

Kazan State Power Engineering University, Russian Federation

Abstract: 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 Coburnís theorem.

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

Full text: PDF file (166 kB)
References: PDF file   HTML file
MSC: 22D05
Received: 25.07.2014
Accepted:15.09.2014
Language:

Citation: K. H. Hovsepyan, “The $C^*$-algebra $\mathfrak{T}_m$ as a crossed product”, Proceedings of the YSU, Physical and Mathematial Scineces, 2014, no. 3, 24–30

Citation in format AMSBIB
\Bibitem{Ovs14}
\by K.~H.~Hovsepyan
\paper The $C^*$-algebra $\mathfrak{T}_m$ as a crossed product
\jour Proceedings of the YSU, Physical and Mathematial Scineces
\yr 2014
\issue 3
\pages 24--30
\mathnet{http://mi.mathnet.ru/uzeru68}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. K. H. Hovsepyan, A. V. Tsutsulyan, “$K$-Groups of some subalgebras of the Toeplitz algebra”, Uch. zapiski EGU, ser. Fizika i Matematika, 51:3 (2017), 224–230  mathnet
    2. Hovsepyan K.H., “Type of Some Nuclear Subalgebras of the Toeplitz Algebra Generated By Inverse Subsemigroups of a Bicyclic Semigroup”, Ukr. Math. J., 69:11 (2018), 1805–1820  crossref  isi
  • Proceedings of the Yerevan State University, series Physical and Mathematical sciences
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