Automorphisms of the Cuntz algebras

Abstract

We survey recent results on endomorphisms and especially on automorphisms of the Cuntz algebras O_n, with a special emphasis on the structure of the Weyl group. We discuss endomorphisms globally preserving the diagonal MASA and their corresponding actions. In particular, we investigate those endomorphisms of O_n which restrict to automorphisms of the diagonal. We review a combinatorial approach to the study of permutative endomorphisms. All the presented material is put in context with current research topics.

arXiv commentSubmitted to the Proceedings of the EU-NCG 4th Annual Meeting, Bucharest 2011

References in corpus (6)

• Hopf Algebras, Renormalization and Noncommutative Geometry
• Quantum Geometry of 3-Dimensional Lattices and Tetrahedron Equation
• Perturbative Quantum Field Theory via Vertex Algebras
• Twisted cyclic theory and an index theory for the gauge invariant KMS state on Cuntz algebras
• Labeled Trees and Localized Automorphisms of the Cuntz Algebras
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Cited by in corpus (1)

• On normalizers of $C^{\ast }$-subalgebras in the Cuntz algebra ${\mathcal{O}}_n$