Representation theory of partial relation extensions
Representation Theory
2019-11-19 v3 Rings and Algebras
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.
Cite
@article{arxiv.1604.01269,
title = {Representation theory of partial relation extensions},
author = {Ibrahim Assem and Juan Carlos Bustamante and Julie Dionne and Patrick Le Meur and David Smith},
journal= {arXiv preprint arXiv:1604.01269},
year = {2019}
}