Conference abstracts

Session S11 - Representations of Algebras

July 25, 15:00 ~ 15:50

Partial relation extensions

Ibrahim Assem

Université de Sherbrooke, Québec, Canada   -

It is well-known that cluster-tilted algebras introduced by Buan, Marsh and Reiten can equivalently be described as relation extensions, that is, trivial extensions of a tilted algebra C by its relation bimodule E. Also, any complete slice in modC embeds as a local slice in the module category of the cluster tilted algebra.

The objective of this talk is to introduce an intermediate class of algebras, called partial relation extensions, where E is replaced by one of its direct summands E'. Our main results show how one can compute the bound quiver and the module category of a partial relation extension. We also prove that a complete slice in modC embeds as local slice in the module category of its partial relation extensions.

Joint work with Juan Carlos Bustamante (Université de Sherbrooke), Julie Dionne (Cégep de Sherbrooke), Patrick Le Meur (Université Paris-Diderot) and David Smith (Bishop's University).

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