Geodesic
On a class of operator algebras generated by a family of partial isometries
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XXVI. Representation theory, dynamical systems, combinatorial methods, Tome 437 (2015), pp. 131-144 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper provides a short overview of a series of articles devoted to the $C^*$-algebra generated by a self-mapping on a countable set. Such an algebra can be seen as a representation of the universal $C^*$-algebra generated by the family of partial isometries satisfying a set of conditions. These conditions are determined by the initial mapping. 
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     title = {On a~class of operator algebras generated by a~family of partial isometries},
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A. Yu. Kuznetsova. On a class of operator algebras generated by a family of partial isometries. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial and algoritmic methods. Part XXVI. Representation theory, dynamical systems, combinatorial methods, Tome 437 (2015), pp. 131-144. http://geodesic.mathdoc.fr/item/ZNSL_2015_437_a6/

[1] S. A. Grigoryan, A. Yu. Kuznetsova, “$C^*$-algebry, porozhdennye otobrazheniyami”, Mat. zametki, 87:5 (2010), 694–703 | DOI | MR | Zbl

[2] S. A. Grigoryan, A. Yu. Kuznetsova, “$AF$-podalgebry $C^*$-algebry, porozhdennoi otobrazheniem”, Izv. vuzov. matem., 2010, no. 3, 82–87 | MR | Zbl

[3] S. A. Grigoryan, A. Yu. Kuznetsova, E. V. Patrin, “Ob odnom kriterii neprivodimosti algebry $C^*_\varphi(X)$”, Izv. NAN Armenii matem., 49:1 (2014), 75–82 | MR

[4] A. Yu. Kuznetsova, “Ob odnom klase $C^*$-algebr, porozhdennykh schetnym semeistvom chastichnykh izometrii”, Izv. NAN Armenii matem., 45:6 (2010), 51–62 | MR | Zbl

[5] B. Blackadar, Operator Algebras, Springer, 2006 | MR | Zbl

[6] N. P. Brown, N. Ozawa, $C^*$-algebras and Finite-Dimensional Approximations, Amer. Math. Soc., Providence, RI, 2008 | MR | Zbl

[7] J. Cuntz, W. Krieger, “A class of $C^*$-algebras and topological Markov chains”, Invent. Math., 56:3 (1980), 251–268 | DOI | MR | Zbl

[8] V. Deaconu, A. Kumjian, P. Muhly, Cohomology of topological graphs and Cuntz–Pimsner algebras, 1999, arXiv: math/9901094v1 | MR

[9] S. Doplicher, C. Pinzari, R. Zuccante, “The $C^*$-algebras of a Hilbert bimodule”, Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8), 1:2 (1998), 263–282 | MR

[10] R. Exel, Circle actions on $C^{*}$-algebras, partial automorphisms and generalized Pimsner–Voiculescu exact sequence, 1992, arXiv: funct-an/9211001v1 | MR

[11] R. Exel, Partial Dynamical Systems, Fell Bundles and Applications, http://mtm.ufsc.br/~exel/papers/pdynsysfellbun.pdf

[12] R. Exel, M. Laca, J. Quigg, Partial dinamical systems and $C^*$-algebras generated by partial izometries, 1997, arXiv: funct-an/9712007 | MR

[13] S. Grigoryan, A. Kuznetsova, “$C^*$-algebras generated by mappings”, Lobachevskii J. Math., 29:1 (2008), 5–8 | DOI | MR | Zbl

[14] S. Grigoryan, A. Kuznetsova, “On a class of nuclear $C^*$-algebras”, An Operator Theory Summer, Proceedings of the 23rd Intenational Conference on Operator Theory (Timisoara, Romania, 2010), 39–50 | MR

[15] S. Grigoryan, A. Kuznetsova, “Torus action on $C^*$-algebra”, The Varied Landscape of Operator Theory, Proceedings of the 24th Intenational Conference on Operator Theory (Timisoara, Romania, 2012), 127–136

[16] A. Kumjian, “Notes on $C^*$-algebras of graphs”, Operator Algebras and Operator Theory, Contemp. Math., 228, Amer. Math. Soc., Providence, RI, 1998, 189–200 | DOI | MR | Zbl

[17] A. Kumjian, On certain Cuntz–Pimsner algebras, 2001, arXiv: math/0108194 | MR

[18] A. Kuznetsova, “$C^*$-algebra generated by mapping which has finite orbits”, Oper. Theory Adv. Appl., 242 (2014), 229–241 | DOI | MR | Zbl

[19] M. Laka, I. Raeburn, “Semigroup crossed products and Toeplitz algebras of nonabelian groups J.”, Funct. Anal., 130 (1995), 77–117 | DOI | MR

[20] K. Matsumoto, “On $C^*$-algebras associated with subshifts”, Internat. J. Math., 8 (1997), 357–374 | DOI | MR | Zbl

[21] K. Matsumoto, “Relation among generators of $C^{*}$-algebras associated with subshifts”, Internat. J. Math., 10 (1999), 385–405 | DOI | MR | Zbl

[22] A. Nica, “$C^*$-algebras generated by isometries and Wiener–Hopf operators”, J. Operator Theory, 27 (1992), 17–52 | MR | Zbl

[23] W. L. Pashke, “$K$-theory for actions of the circle group on $C^*$-algebras”, J. Operator Theory, 6 (1981), 125–133 | MR

[24] M. V. Pimsner, “A class of $C^*$-algebras generalizing both Cuntz–Krieger algebras and crossed products by $\mathbb Z$”, Fields Inst. Commun., 12 (1997), 189–212 | MR | Zbl

[25] I. Raeburn,, Graph Algebras, Amer. Math. Soc., Providence, RI, 2000