- 08/03/2023 - 15h - CLAV Anfiteatro 1
Carlos Ramos, Universidade de Évora
The Cuntz-Krieger algebras, 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.
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)
