Abstract
We study the representation theory of C*-algebras by using semigroup theory and automata theory. The Cuntz algebra [Formula: see text] is a finitely generated, infinite-dimensional, noncommutative C*-algebra. A certain class of cyclic representations of [Formula: see text] is characterized by words from the alphabet 1,…,N, which is called a cycle. A class of endomorphisms of [Formula: see text] is defined by polynomial functions in canonical generators and their conjugates. Such an endomorphism ρ of [Formula: see text] transforms a cycle π to π ◦ ρ which is a direct sum of cycles π1,…,πn unique up to unitary equivalence. The passage from π to π1,…,πn is called a branching law for ρ. In this article, we construct a Mealy machine from the endomorphism in order to compute its branching law. We show that the branching law is obtained as outputs from the machine for the input information of a given representation. Furthermore the actual computation of the branching law is executed by using a generalized de Bruijn graph associated with the Mealy machine.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
