Algebras from surfaces without punctures

DOI10.1016/j.jalgebra.2011.10.034zbMath1246.13034arXiv1103.4357OpenAlexW2962689304MaRDI QIDQ420725

Lucas David-Roesler, Ralf Schiffler

Publication date: 23 May 2012

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1103.4357

zbMATH Keywords

tilting theorygentle algebrabordered surface with marked points

Mathematics Subject Classification ID

Related Items (21)

Derived invariants for surface algebras ⋮ A Geometric Model for the Module Category of a Gentle Algebra ⋮ The derived category of surface algebras: the case of the torus with one boundary component ⋮ Endomorphism algebras for a class of negative Calabi-Yau categories ⋮ Maximal rigid objects as noncrossing bipartite graphs ⋮ On the Lie algebra structure of the first Hochschild cohomology of gentle algebras and Brauer graph algebras ⋮ A geometric model for the module category of a skew-gentle algebra ⋮ A complete derived invariant for gentle algebras via winding numbers and Arf invariants ⋮ A geometric realization of socle-projective categories for posets of type \(\mathbb{A}\) ⋮ From the potential to the first Hochschild cohomology group of a cluster tilted algebra ⋮ A \(\tau\)-tilting approach to dissections of polygons ⋮ Injective presentations of induced modules over cluster-tilted algebras ⋮ Derived equivalence of surface algebras in genus 0 via graded equivalence. ⋮ Oriented flip graphs of polygonal subdivisions and noncrossing tree partitions ⋮ Induced and coinduced modules over cluster-tilted algebras ⋮ Higher extensions for gentle algebras ⋮ Non-kissing and non-crossing complexes for locally gentle algebras ⋮ Trivial extensions of gentle algebras and Brauer graph algebras. ⋮ Derived invariants for surface cut algebras of global dimension 2 II: the punctured case ⋮ Non-kissing versus non-crossing ⋮ Brauer Graph Algebras

Cites Work

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• Positivity for cluster algebras from surfaces
• From iterated tilted algebras to cluster-tilted algebras.
• Cluster categories for algebras of global dimension 2 and quivers with potential.
• On cluster algebras arising from unpunctured surfaces. II
• Gentle algebras arising from surface triangulations.
• Cluster algebras and triangulated surfaces. I: Cluster complexes
• Quivers with potentials and their representations. I: Mutations.
• Iterated tilted algebras of type \({\tilde {\mathbb A}}_ n\)
• Combinatorial derived invariants for gentle algebras.
• Tilting theory and cluster combinatorics.
• Algebras of acyclic cluster type: Tree type and typeÃ
• On Cluster Algebras Arising from Unpunctured Surfaces
• Cluster-tilted algebras
• Quivers with potentials associated to triangulated surfaces
• Auslander-reiten sequences with few middle terms and applications to string algebrass
• Cluster Algebras and Triangulated Surfaces Part II: Lambda Lengths
• THE ALGEBRAS DERIVED EQUIVALENT TO GENTLE CLUSTER TILTED ALGEBRAS
• Cluster-tilted algebras as trivial extensions
• Quivers with relations arising from clusters (𝐴_{𝑛} case)

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