Multiplicative bases and deformations of representation-finite algebras
Bautista, Gabriel, Roiter, and Salmer\'on proved that every finite-dimensional representation-finite algebra over an algebraically closed field admits a multiplicative basis, in which products of basis elements are zero or basis elements. Outside characteristic two, they also proved that such an algebra is standard: its category of indecomposable modules is presented by its Auslander--Reiten quiver and mesh relations. We give another proof of both theorems. For a basic algebra, grading morphisms between indecomposable modules by powers of the categorical radical and restricting to…
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