New York Journal of Mathematics
Volume 24a (2018), 56-86


Kenneth R. Davidson, Adam H. Fuller, and Evgenios T.A. Kakariadis

Semicrossed products of operator algebras: a survey

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Published: November 7, 2018.
Keywords: Dynamical systems of operator algebras, semicrossed products, C*-envelope, C*-crossed products.
Subject: 47A20, 47L25, 47L65, 46L07.

Semicrossed product algebras have been used to study dynamical systems since their introduction by Arveson in 1967. In this survey article, we discuss the history and some recent work, focussing on the conjugacy problem, dilation theory and C*-envelopes, and some connections back to the dynamics.


First author partially supported by NSERC, Canada. Third author partially supported by the Kreitman Foundation Post-doctoral Fellow Scholarship, and the Skirball Foundation via the Center for Advanced Studies in Mathematics at Ben-Gurion University of the Negev.

Author information

Kenneth R. Davidson:
Pure Mathematics Department
University of Waterloo
Waterloo, ON N2L-3G1, Canada


Adam H. Fuller:
Mathematics Department
University of Nebraska-Lincoln
Lincoln, NE 68588, USA
Current address: Department of Mathematics
Ohio University
Athens, OH 45701, USA


Evgenios T.A. Kakariadis:
Department of Mathematics
Ben-Gurion University of the Negev
Be'er Sheva 84105, Israel
Current address: School of Mathematics, Statistics and Physics
Newcastle University
Newcastle upon Tyne, NE1 7RU, UK