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Endomorphisms of the Cuntz algebras

Roberto Conti, Jeong Hee Hong, Wojciech Szymański (2011)

Banach Center Publications

This mainly expository article is devoted to recent advances in the study of dynamical aspects of the Cuntz algebras 𝓞ₙ, n < ∞, via their automorphisms and, more generally, endomorphisms. A combinatorial description of permutative automorphisms of 𝓞ₙ in terms of labelled, rooted trees is presented. This in turn gives rise to an algebraic characterization of the restricted Weyl group of 𝓞ₙ. It is shown how this group is related to certain classical dynamical systems on the Cantor set. An identification...

Entropy for a pair of subalgebras via automorphisms.

Choda, Marie (2010)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

Ergodic Actions by Compact Groups on C*-Algebras.

Sergio Alberverio, Raphael Hoegh-Krohn (1980)

Mathematische Zeitschrift

Erratum to "Tracial states on crossed products associated with Furstenberg transformations on the 2-torus" (Studia Math. 115 (1995), 183-187)

Kazunori Kodaka (1996)

Studia Mathematica

Explicit computations of all finite index bimodules for a family of II $_{1}$ factors

Stefaan Vaes (2008)

Annales scientifiques de l'École Normale Supérieure

We study II $_{1}$ factors $M$ and $N$ associated with good generalized Bernoulli actions of groups having an infinite almost normal subgroup with the relative property (T). We prove the following rigidity result : every finite index $M$ - $N$ -bimodule (in particular, every isomorphism between $M$ and $N$ ) is described by a commensurability of the groups involved and a commensurability of their actions. The fusion algebra of finite index $M$ - $M$ -bimodules is identified with an extended Hecke fusion algebra, providing the...