2022/06/09 by Fernandez, Elsa, Schroll, Sibylle, Treffinger, Hipolito +2
#FOS: Mathematics #Representation Theory (math.RT) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2206.04581
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.