Characterisations of trivial extensions
Rings and Algebras
2022-06-22 v2 Representation Theory
Abstract
In this paper we give a characterisation of trivial extension algebras in terms of quivers with relations. This result is based on a explicit description of the ideal of relations of the trivial extension of an algebra, given by the first author in the appendix. We also give a new proof of Wakamatsu's theorem in terms of their quiver and relations, which determines when two given algebras have isomorphic trivial extensions.
Cite
@article{arxiv.2206.04581,
title = {Characterisations of trivial extensions},
author = {Elsa Fernandez and Sibylle Schroll and Hipolito Treffinger and Sonia Trepode and Yadira Valdivieso},
journal= {arXiv preprint arXiv:2206.04581},
year = {2022}
}
Comments
17 pages. Comments welcome