Roberto Conti (Rom)
Automorphisms of the Cuntz algebras and their Weyl groups. A case study.
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 probably the most studied class of C*-algebras ever. Notably, the
study of their automorphisms reveals 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.