Geodesic
On the extension of the Toeplitz algebra
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 154 (2012) no. 4, pp. 130-138

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We study the $C^*$-extensions of the Toeplitz algebras with the assistance of isometric operators. It is shown that in the case when the Toeplitz algebra acts irreducibly, all such $C^*$-extensions generate the same algebra, i.e., there is no non-trivial extension of the Toeplitz algebra. We provide the examples of the non-trivial extensions of the Toeplitz algebra in the case when its representation is reducible.
Keywords: inverse semigroup, inverse representation, Toeplitz algebra, $\pi$-extension, inverse $\pi$-extension, $C^*$-algebra. 
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     title = {On the extension of the {Toeplitz} algebra},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
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     number = {4},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/UZKU_2012_154_4_a10/}
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T. A. Grigoryan; E. V. Lipacheva; V. A. Tepoyan. On the extension of the Toeplitz algebra. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 154 (2012) no. 4, pp. 130-138. http://geodesic.mathdoc.fr/item/UZKU_2012_154_4_a10/