- 08/03/2023 - 15h - CLAV Anfiteatro 1

**Carlos Ramos**, Universidade de Évora

The Cuntz-Krieger algebras,

Let

We consider the problem of deciding when a restriction

Using certain representations arising from the orbits of

*O_A*, are C*-algebras generated by n partial isometries, subject to certain relations codified by a 0-1 matrix*A*, with*n*=dim*A*.Let

*M*(*I*) be a certain class of Markov interval maps with domain contained in the interval*I*, whose associated transition matrix*A*_*f*, necessarily primitive, codifies the possible transitions between the Markov states.We consider the problem of deciding when a restriction

*g*:=*f*|_*J*of a map*f*in*M*(*I*) to a subset*J*of*I*is in the class*M*([*J*]), where [*J*] is the minimal closed interval containing*J*. We establish natural conditions on*J*so that*g*=*f*|_*J*is a Markov map. Then we tackle the central problem of deciding when the matrix*A*_*g*is primitive in this framework. We are able to enumerate the sets*J*, satisfying the referred conditions, through a systematic process of elimination of the rows/columns of the state splitting of*A*_*f*associated to the so called removable states, which ensures the primitivity of the matrices*A*_*g*.Using certain representations arising from the orbits of

*f*and*g*, we obtain a classification scheme for the sub algebras of*O*_*A*, with*A*primitive, which are also Cuntz-Krieger algebras.joint work with Paulo Pinto, Nuno Martins (IST)