Geodesic
On $\pi$-extensions of the semigroup $\mathbb{Z}_+$
Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 1 (2013), pp. 3-5.

Voir la notice de l'article provenant de la source Math-Net.Ru

In the paper inverse $\pi$-extensions of the semigroup $\mathbb{Z}_+$ are studied. It is shown that $pi$-extension of the semigroup $\mathbb{Z}_+$ is inverse, if and only if its $\pi$-extension coincides with $\pi(\mathbb{Z}_+)$. The existence of a non-inverse $\pi$-extension for any abelian semigroup is proved.
Keywords: inverse semigroup, inverse representation, $\pi$-extension, Toeplitz algebra, $C^*$-algebra, inverse $\pi$-extension. 
@article{UZERU_2013_1_a0,
     author = {T. A. Grigoryan and E. V. Lipacheva and V. H. Tepoyan},
     title = {On $\pi$-extensions of the semigroup $\mathbb{Z}_+$},
     journal = {Proceedings of the Yerevan State University. Physical and mathematical sciences},
     pages = {3--5},
     publisher = {mathdoc},
     number = {1},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UZERU_2013_1_a0/}
}
TY  - JOUR
AU  - T. A. Grigoryan
AU  - E. V. Lipacheva
AU  - V. H. Tepoyan
TI  - On $\pi$-extensions of the semigroup $\mathbb{Z}_+$
JO  - Proceedings of the Yerevan State University. Physical and mathematical sciences
PY  - 2013
SP  - 3
EP  - 5
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/UZERU_2013_1_a0/
LA  - en
ID  - UZERU_2013_1_a0
ER  - 
%0 Journal Article
%A T. A. Grigoryan
%A E. V. Lipacheva
%A V. H. Tepoyan
%T On $\pi$-extensions of the semigroup $\mathbb{Z}_+$
%J Proceedings of the Yerevan State University. Physical and mathematical sciences
%D 2013
%P 3-5
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/UZERU_2013_1_a0/
%G en
%F UZERU_2013_1_a0
T. A. Grigoryan; E. V. Lipacheva; V. H. Tepoyan. On $\pi$-extensions of the semigroup $\mathbb{Z}_+$. Proceedings of the Yerevan State University. Physical and mathematical sciences, no. 1 (2013), pp. 3-5. http://geodesic.mathdoc.fr/item/UZERU_2013_1_a0/

[1] L.A. Coburn, “The $C^*$-Algebra Generated by an Isometry”, Bull. Amer. Math. Soc., 73 (1967), 722–726 | DOI | MR | Zbl

[2] R.G. Douglas, “On the $C^*$-Algebra of a One-Parameter Semigroup of Isometries”, Acta Math., 128 (1972), 143–152 | DOI | MR

[3] G.J. Murphy, “Ordered Groups and Toeplitz Algebras”, J. Operator Theory, 18 (1987), 303–326 | MR | Zbl

[4] S.Y. Jang, “Generalized Toeplitz Algebras of a Certain Non-Amenable Semigroup”, Bull. Korean Math. Soc., 43:2 (2006), 333–341 | DOI | MR

[5] I. Raeburn, S.T. Vittadello, “The Isometric Representation Theory of a Perforated Semigroup”, J. Operator Theory, 62:2 (2009), 357–370 | MR | Zbl

[6] M.A. Aukhadiev, V.H. Tepoyan, “Isometric Representations of Totally Ordered Semigroups”, Lobachevskii J. of Mat., 33 (2012), 239–243 | DOI | MR | Zbl

[7] S.A. Grigoryan, A.F. Salakhutdinov, “$C^*$-Algebra Generated by Cancellative Semigroups”, Sibirsk. Mat. Zh., 51:1 (2010), 16–25 | MR | Zbl