The York Research Database

Jones and the second author have discovered in [4] that certain representations of the so-called polycyclic monoids are closely related to the representations of the Cuntz algebras Cn studied by Bratteli and Jorgenssen in [2]. We investigate these representations of the polycyclic monoids, generalise some results from [4], give a (sharp) upper bound on the number of atoms in case one of the parameters tends to infinity and present an infinite family of representations having only one atom. Furthermore, by making use of a C++ program we present some observations regarding the ratio of atoms to the number of possible atoms in the n = 3 case.