We associate an algebra A (Γ) to a triangulation Γ of a surface S with a set of boundary
marking points. This algebra A (Γ) is gentle and Gorenstein of dimension one. We also prove …

In this article, gentle algebras are realised as tiling algebras, which are associated to partial
triangulations of unpunctured surfaces with marked points on the boundary. This notion of …

Gentle algebras are in bijection with admissible dissections of marked oriented surfaces. In
this paper, we further study the properties of admissible dissections and we show that silting …

This survey starts with a motivation of the study of Brauer graph algebras by relating them to
special biserial algebras. The definition of Brauer graph algebras is given in great detail with …

We show that two well-studied classes of tame algebras coincide: namely, the class of
symmetric special biserial algebras coincides with the class of Brauer graph algebras. We …

We define derived equivalent invariants for gentle algebras, constructed in an easy
combinatorial way from the quiver with relations defining these algebras. Our invariants …

We determine the singularity category of an arbitrary finite‐dimensional gentle algebra Λ. It
is a finite product of n‐cluster categories of type A 1. Equivalently, it may be described as the …

A gentle algebra gives rise to a dissection of an oriented marked surface with boundary into
polygons and the bounded derived category of the gentle algebra has a geometric …

We study triangulated categories which can be modeled by an oriented marked surface
$\mathcal {S} $ and a line field $\eta $ on $\mathcal {S} $. This includes bounded derived …

Discrete derived categories were studied initially by Vossieck (J Algebra 243: 168–176,
2001) and later by Bobiński et al.(Cent Eur J Math 2: 19–49, 2004). In this article, we …