Skip Navigation

Journal of the London Mathematical Society 2000 61(3):893-904; doi:10.1112/S0024610799008492
© 2000 by London Mathematical Society
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Laca, M.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The London Mathematical Society

From Endomorphisms to Automorphisms and Back: Dilations and Full Corners

Marcelo Laca

Department of Mathematics, University of Newcastle NSW 2308, Australia, marcelo{at}math.newcastle.edu.au

Received 10 February 1998. Revision received 19 October 1998.

When S is a discrete subsemigroup of a discrete group G such that G = S–1S, it is possible to extend circle-valued multipliers from S to G, to dilate (projective) isometric representations of S to (projective) unitary representations of G, and to dilate/extend actions of S by injective endomorphisms of a C*-algebra to actions of G by automorphisms of a larger C*-algebra. These dilations are unique provided they satisfy a minimality condition. The (twisted) semigroup crossed product corresponding to an action of S is isomorphic to a full corner in the (twisted) crossed product by the dilated action of G. This shows that crossed products by semigroup actions are Morita equivalent to crossed products by group actions, making powerful tools available to study their ideal structure and representation theory. The dilation of the system giving the Bost–Connes Hecke C*-algebra from number theory is constructed explicitly as an application: it is the crossed product C0(Af){rtimes}Q*+, corresponding to the multiplicative action of the positive rationals on the additive group Af of finite adeles.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.