A new look at the crossed-product of a C*-algebra by an endomorphism
By R. Exel. Ergodic Theory and Dynamical Systems, 2000
184 citations recorded by the source corpus.
We give a new definition for the crossed-product of a C*-algebra A by a *-endomorphism $\alpha$, which depends not only on the pair $(A,\alpha)$ but also on the choice of a transfer operator. With this we generalize some of the earlier constructions in the situations in which they behave best (e.g. for monomorphisms with hereditary range), but we get a different and perhaps more natural outcome in other situations. For example, we show that the Cuntz–Krieger algebra $\mathcal{O}_{\mathcal A}$ arises as the result of our construction when applied to the corresponding Markov subshift and a very natural transfer operator.
Subfields: Algebra and Number Theory, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/d7bb13ea9b91a556499749db3ad07f18ee37c64e
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
In Mathematical Physics
Citations in the corpus
- Fractional skew monoid rings (2003, background): “…group ring A ∗α G can also be defined as the unital ring R such that there are a unital ring homomorphism φ : A → R and a unital monoid homomorphism i : G→ R from G to the multiplicative structure of R, universal with respect to the property that i(g)φ(a) = φ(αg(a))i(g) for all a ∈ A and all g ∈ G.”
- Hardy algebras, W*-correspondences and interpolation theory (2003, background): “The operator S is closely related to what is called a transfer operator or a Ruelle operator in [9] and [17].”
- ${{C}^{*}}$ -Algebras of Irreversible Dynamical Systems (2002, background): “In a recent article [11] the first named author has proposed yet another construction of crossed product in the irreversible setting (see also [12], [13]), the ingredients of which are a unital C*-algebra A, an injective *-endomorphism”
- Semicrossed Products of Operator Algebras by Semigroups (2014, methodology): “Before we proceed to the presentation of the main results we mention that there is a substantial literature on the examination of semigroup actions that involves the existence of transfer operators, e.g., the works of Brownlowe-Raeburn [17], Brownlowe-Raeburn-Vittadello [18], Exel [46], Exel-Renault”