Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 39
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Kakariadis, Evgenios T. A. 2016. On Nica-Pimsner Algebras of C*-Dynamical Systems Over $\mathbb{Z}_+^n$. International Mathematics Research Notices, p. rnw050.

    KAKARIADIS, EVGENIOS T. A. and PETERS, JUSTIN R. 2016. ERGODIC EXTENSIONS OF ENDOMORPHISMS. Bulletin of the Australian Mathematical Society, Vol. 93, Issue. 02, p. 307.

    Kwaśniewski, B.K. 2016. Crossed products by endomorphisms of C0(X)-algebras. Journal of Functional Analysis, Vol. 270, Issue. 6, p. 2268.

    Kwaśniewski, B. K. 2015. Extensions of C*-dynamical systems to systems with complete transfer operators. Mathematical Notes, Vol. 98, Issue. 3-4, p. 419.

    Kwaśniewski, Bartosz Kosma 2015. Ideal structure of crossed products by endomorphisms via reversible extensions of C*-dynamical systems. International Journal of Mathematics, Vol. 26, Issue. 03, p. 1550022.

    Stammeier, Nicolai 2015. On C*-algebras of irreversible algebraic dynamical systems. Journal of Functional Analysis, Vol. 269, Issue. 4, p. 1136.

    Afsar, Zahra an Huef, Astrid and Raeburn, Iain 2014. KMS states on C*-algebras associated to local homeomorphisms. International Journal of Mathematics, Vol. 25, Issue. 08, p. 1450066.

    Hamada, Hiroyasu 2014. Quotient Algebras of Toeplitz-Composition $$C^{*}$$ C ∗ -Algebras for Finite Blaschke Products. Complex Analysis and Operator Theory, Vol. 8, Issue. 4, p. 843.

    Kwaśniewski, B. K. 2014. Crossed Products for Interactions and Graph Algebras. Integral Equations and Operator Theory, Vol. 80, Issue. 3, p. 415.

    Laca, Marcelo Raeburn, Iain Ramagge, Jacqui and Whittaker, Michael F. 2014. Equilibrium states on the Cuntz–Pimsner algebras of self-similar actions. Journal of Functional Analysis, Vol. 266, Issue. 11, p. 6619.

    Brownlowe, Nathan and Raeburn, Iain 2013. Two families of Exel–Larsen crossed products. Journal of Mathematical Analysis and Applications, Vol. 398, Issue. 1, p. 68.

    Cuntz, Joachim and Vershik, Anatoly 2013. C*-Algebras Associated with Endomorphisms and Polymorphisms of Compact Abelian Groups. Communications in Mathematical Physics, Vol. 321, Issue. 1, p. 157.

    Kwaśniewski, B.K. and Lebedev, A.V. 2013. Crossed products by endomorphisms and reduction of relations in relative Cuntz–Pimsner algebras. Journal of Functional Analysis, Vol. 264, Issue. 8, p. 1806.

    Ramos, C. Correia Martins, Nuno and Pinto, Paulo R. 2013. On C*-Algebras from Interval Maps. Complex Analysis and Operator Theory, Vol. 7, Issue. 1, p. 221.

    an Huef, Astrid and Raeburn, Iain 2012. Stacey Crossed Products Associated to Exel Systems. Integral Equations and Operator Theory, Vol. 72, Issue. 4, p. 537.

    BROWNLOWE, NATHAN AN HUEF, ASTRID LACA, MARCELO and RAEBURN, IAIN 2012. Boundary quotients of the Toeplitz algebra of the affine semigroup over the natural numbers. Ergodic Theory and Dynamical Systems, Vol. 32, Issue. 01, p. 35.

    Courtney, Dennis Muhly, Paul S. and Schmidt, Samuel W. 2012. Composition Operators and Endomorphisms. Complex Analysis and Operator Theory, Vol. 6, Issue. 1, p. 163.

    Davidson, K. R. and Kakariadis, E. T. A. 2012. Conjugate Dynamical Systems on C*-algebras. International Mathematics Research Notices,

    Kwaśniewski, Bartosz K 2012. C*-algebras associated with reversible extensions of logistic maps. Sbornik: Mathematics, Vol. 203, Issue. 10, p. 1448.

    Larsen, Nadia S. and Li, Xin 2012. The 2-adic ring <mml:math altimg="si1.gif" overflow="scroll" xmlns:xocs="" xmlns:xs="" xmlns:xsi="" xmlns="" xmlns:ja="" xmlns:mml="" xmlns:tb="" xmlns:sb="" xmlns:ce="" xmlns:xlink="" xmlns:cals=""><mml:msup><mml:mi>C</mml:mi><mml:mo>⁎</mml:mo></mml:msup></mml:math>-algebra of the integers and its representations. Journal of Functional Analysis, Vol. 262, Issue. 4, p. 1392.

  • Ergodic Theory and Dynamical Systems, Volume 23, Issue 6
  • December 2003, pp. 1733-1750

A new look at the crossed-product of a C*-algebra by an endomorphism

  • RUY EXEL (a1)
  • DOI:
  • Published online: 01 December 2003

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.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Ergodic Theory and Dynamical Systems
  • ISSN: 0143-3857
  • EISSN: 1469-4417
  • URL: /core/journals/ergodic-theory-and-dynamical-systems
Please enter your name
Please enter a valid email address
Who would you like to send this to? *