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

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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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     author = {A. Yu. Kuznetsova},
     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/