Seminari del Dipartimento di Matematica

Seminario del 2023

Symmetries of the Cuntz algebras

algebra e geometria

analisi matematica

fisica matematica

Finite multiplets of isometries with orthogonal ranges summing up to 1 were systematically used by Doplicher and Roberts in the early 70's in their study of the superselection structure of Quantum Field Theory. Nowadays, the C*-algebra generated by any such multiplet is known as Cuntz algebra O_n, where n is the cardinality of the given multiplet. Since their introduction, Cuntz algebras have been the subject of endless investigations, from many different points of view. They are perhaps the most studied/used class of C*-algebras ever. Notably, the study of their automorphisms presents many challenging facets, where operator algebras meet Lie theory, dynamical systems and combinatorics. We will present an overview of recent results, along with some open questions.