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

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 Coburn’s theorem.

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

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MSC: 22D05
Accepted:15.09.2014
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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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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
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
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