A model for the canonical algebras of bimodules type (1, 4) over truncated polynomial rings

Abstract Let C (\! () \!) C ( (ε) ) be the field of complex Laurent series. We use Galois descent techniques to show that the simple regular representations of the species of type (1, \, 4) (1, 4) over C (\! () \!) C ( (ε) ) are naturally parametrized by the closed points of Spec (C (\! () \!) x) ̇\1, \, 2\ Spec (C ( (ε) ) x) ∪ ˙ 1, 2. Moreover, we provide weak normal forms for those representations. We use our representatives of the simple regular representations to describe the canonical algebras associated to the species of type (1, 4) over C (\! () \!) C ( (ε) ). This suggests a model of those algebras in the sense of the work of Geiss et al. (Invent Math 209 (1): 61–158, 2017; Math Z 295: 1245–1277, 2020).