English

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.

Keywords

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

R2 v1 2026-06-24T11:45:20.998Z