Skip Navigation


Bulletin of the London Mathematical Society Advance Access originally published online on March 12, 2008
Bulletin of the London Mathematical Society 2008 40(1):151-162; doi:10.1112/blms/bdm107
This Article
Right arrow Full Text (PDF)
Right arrow All Versions of this Article:
40/1/151    most recent
bdm107v1
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 Similar articles in ISI Web of Science
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrow Search for citing articles in:
ISI Web of Science (1)
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Assem, I.
Right arrow Articles by Schiffler, R.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© 2008 London Mathematical Society

Cluster-tilted algebras as trivial extensions

I. Assem

Département de Mathématiques
Université de Sherbrooke
Sherbrooke, Québec
Canada J1K 2R1
ibrahim.assem@usherbrooke.ca

T. Brüstle

Département de Mathématiques
Université de Sherbrooke
Sherbrooke, Québec
Canada J1K 2R1
and
Department of Mathematics
Bishop's University
Lennoxville, Québec
Canada J1M 1Z7
tbruestl@ubishops.ca

R. Schiffler

Department of Mathematics and Statistics
University of Massachusetts at Amherst
Amherst, MA 01003-9305
USA
schiffler@math.umass.edu

Received 22 January 2006. Revision received 20 March 2007.

Given a finite-dimensional algebra C (over an algebraically closed field) of global dimension at most two, we define its relation-extension algebra to be the trivial extension C ExtFormula(DC,C) of C by the C–C-bimodule ExtFormula(DC,C). We give a construction for the quiver of the relation-extension algebra in case the quiver of C has no oriented cycles. Our main result says that an algebra C is cluster-tilted if and only if there exists a tilted algebra C such that C is isomorphic to the relation-extension of C.

2000 Mathematics Subject Classification 16S70 (primary), 16G20 (secondary).

The first and the second author gratefully acknowledge partial support form the NSERC of Canada. The second author also thanks the universities of Sherbrooke and Bishop's for partial support. The third author was partially supported by the University of Massachusetts.


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.