Jump to ContentJump to Main Navigation
Show Summary Details

Journal für die reine und angewandte Mathematik

Managing Editor: Weissauer, Rainer

Ed. by Colding, Tobias / Cuntz, Joachim / Huybrechts, Daniel / Hwang, Jun-Muk

12 Issues per year

IMPACT FACTOR increased in 2015: 1.616
5-year IMPACT FACTOR: 1.690
Rank 18 out of 312 in category Mathematics in the 2015 Thomson Reuters Journal Citation Report/Science Edition

SCImago Journal Rank (SJR) 2015: 3.614
Source Normalized Impact per Paper (SNIP) 2015: 1.901
Impact per Publication (IPP) 2015: 1.302

Mathematical Citation Quotient (MCQ) 2015: 1.53

See all formats and pricing
Volume 2008, Issue 621 (Jan 2008)


Isomorphisms between topological conjugacy algebras

Kenneth R. Davidson
  • Pure Mathematics Department, University of Waterloo, Waterloo, ON N2L–3G1, Canada. e-mail: krdavids@uwaterloo.ca
/ Elias G. Katsoulis
  • Department of Mathematics, East Carolina University, Greenville, NC 27858, USA. e-mail: KatsoulisE@mail.ecu.edu
Published Online: 2008-07-01 | DOI: https://doi.org/10.1515/CRELLE.2008.057


A family of algebras, which we call topological conjugacy algebras, is associated with each proper continuous map on a locally compact Hausdorff space. Assume that is a continuous proper map on a locally compact Hausdorff space , for i= 1,2. We show that the dynamical systems and are conjugate if and only if some topological conjugacy algebra of is isomorphic as an algebra to some topological conjugacy algebra of . This implies as a corollary the complete classification of the semicrossed products , which was previously considered by Arveson and Josephson [W. Arveson, K. Josephson, Operator algebras and measure preserving automorphisms II, J. Funct. Anal. 4 (1969), 100–134.], Peters [J. Peters, Semicrossed products of C*-algebras, J. Funct. Anal. 59 (1984), 498–534.], Hadwin and Hoover [D. Hadwin, T. Hoover, Operator algebras and the conjugacy of transformations, J. Funct. Anal. 77 (1988), 112–122.] and Power [S. Power, Classification of analytic crossed product algebras, Bull. London Math. Soc. 24 (1992), 368–372.]. We also obtain a complete classification of all semicrossed products of the form , where denotes the disc algebra and a continuous map which is analytic on the interior. In this case, a surprising dichotomy appears in the classification scheme, which depends on the fixed point set of η. We also classify more general semicrossed products of uniform algebras.

About the article

Received: 2006-06-13

Published Online: 2008-07-01

Published in Print: 2008-08-01

Citation Information: Journal für die reine und angewandte Mathematik (Crelles Journal), ISSN (Online) 1435-5345, ISSN (Print) 0075-4102, DOI: https://doi.org/10.1515/CRELLE.2008.057. Export Citation

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

Evgenios T.A. Kakariadis and Elias G. Katsoulis
Journal of Functional Analysis, 2012, Volume 262, Number 7, Page 3108

Comments (0)

Please log in or register to comment.
Log in