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Homological dimensions of gentle algebras via geometric models
Let A = kQ/I be a finite-dimensional basic algebra over an algebraically closed field k which is a gentle algebra with the marked ribbon surface
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A complete derived invariant for gentle algebras via winding numbers and Arf invariants
Gentle algebras are in bijection with admissible dissections of marked oriented surfaces. In this paper, we further study the properties of...
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Triangulations of flow polytopes, ample framings, and gentle algebras
The cone of nonnegative flows for a directed acyclic graph (DAG) is known to admit regular unimodular triangulations induced by framings of the DAG....
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Complete gentle and special biserial algebras are g-tame
The g -vectors of two-term presilting complexes are important invariants. We study a fan consisting of all g -vector cones for a complete gentle...
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Gentle Algebras Arising from Surfaces with Orbifold Points of Order 3, Part I: Scattering Diagrams
To each triangulation of any surface with marked points on the boundary and orbifold points of order three, we associate a quiver (with loops) with...
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A geometric realization of silting theory for gentle algebras
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...
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String and Band Complexes Over String Almost Gentle Algebras
We give a combinatorial description of a family of indecomposable objects in the bounded derived categories of two new classes of algebras: string...
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Schemes of modules over gentle algebras and laminations of surfaces
We study the affine schemes of modules over gentle algebras. We describe the smooth points of these schemes, and we also analyze their irreducible...
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On String Algebras and the Cohen–Macaulay Auslander Algebras
The Cohen–Macaulay Auslander algebra of an algebra A is defined as the endomorphism algebra of the direct sum of all indecomposable Gorenstein...
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A geometric model for the module category of a skew-gentle algebra
In this article, we realize skew-gentle algebras as skew-tiling algebras associated to admissible partial triangulations of punctured marked...
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The Geometric Model of Gentle One-Cycle Algebras
In this paper, we mainly study the geometric model of the derived category of gentle one-cycle algebras provided by Opper, Plamondon and Schroll. We...
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Exceptional sequences in the derived category of a gentle algebra
In this paper, using the correspondence of gentle algebras and dissections of marked surfaces, we study full exceptional sequences in the perfect...
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τ-tilting Finiteness of Biserial Algebras
We compare the notions of τ -tilting finiteness and representation-finiteness of the biserial algebras. In particular, we treat the minimal...
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Tubes containing string modules in symmetric special multiserial algebras
Symmetric special multiserial algebras are algebras that correspond to decorated hypergraphs with orientation, called Brauer configurations. In this...
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Homotopy prefactorization algebras
We apply the theory of operadic Koszul duality to provide a cofibrant resolution of the colored operad whose algebras are prefactorization algebras...
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Classifying Recollements of Derived Module Categories for Derived Discrete Algebras
We study a class of derived discrete Nakayama algebras. All indecomposable compact objects in the derived module category are determined and all...
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Dessins D’Enfants, Brauer Graph Algebras and Galois Invariants
In this paper, we associate a finite dimensional algebra, called a Brauer graph algebra, to every clean dessin d’enfant by constructing a quiver...
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The Derived-Discrete Algebras Over the Real Numbers
We classify derived-discrete algebras over the real numbers up to Morita equivalence, using the classification of complex derived-discrete algebras...
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A Simple Homological Characterization of String Algebras of Finite Representation Type
We prove that among the finite-dimensional algebras of finite representation type those that are string algebras are precisely the ones that have the...