Representation theory of partial relation extensions
Ibrahim Assem, Juan Carlos Bustamante, Julie Dionne, Patrick Le Meur, David Smith
Colloquium Mathematicum 155 (2019), 157-186
MSC: Primary 16G10; Secondary 16G70, 16E30.
DOI: 10.4064/cm7511-3-2018
Published online: 8 November 2018
Abstract
Let $C$ be a finite dimensional algebra of global dimension at most two. A partial relation extension is any trivial extension of $C$ by a direct summand of its relation $C$-$C$-bimodule. When $C$ is a tilted algebra, this construction provides an intermediate class of algebras between tilted and cluster tilted algebras. The text investigates the representation theory of partial relation extensions. When $C$ is tilted, any complete slice in the Auslander–Reiten quiver of $C$ embeds as a local slice in the Auslander–Reiten quiver of the partial relation extension. Moreover, a systematic way of producing partial relation extensions is introduced by considering direct sum decompositions of the potential arising from a minimal system of relations of $C$.
Authors
- Ibrahim AssemDépartement de Mathématiques
Université de Sherbrooke
Sherbrooke, Québec, Canada J1K 2R1
e-mail
- Juan Carlos BustamanteDépartement de Mathématiques
Université de Sherbrooke
Sherbrooke, Québec, Canada J1K 2R1
Current address:
Mathematics Department
Champlain College – Lennoxville
2580 Rue College
Sherbrooke, Québec, Canada J1M 2K3
e-mail
- Julie Dionne—
e-mail
- Patrick Le MeurLaboratoire de Mathématiques
Université Blaise Pascal \& CNRS
Complexe Scientifique Les Cézeaux
BP 80026
63171 Aubière Cedex, France
Current adress:
Université Paris Diderot, Sorbonne Université
CNRS, Institut de Mathématiques de Jussieu-Paris Rive Gauche
IMJ-PRG
F-75013 Paris, France
e-mail
- David SmithDepartment of Mathematics
Bishop’s University
Sherbrooke, Québec, Canada J1M 1Z7
e-mail
