Trivial extensions of gentle algebras and Brauer graph algebras.

DOI10.1016/j.jalgebra.2015.07.037zbMath1330.16010arXiv1405.6419OpenAlexW1891580424MaRDI QIDQ745154

Sibylle Schroll

Publication date: 13 October 2015

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

Full work available at URL: https://arxiv.org/abs/1405.6419

zbMATH Keywords

triangulationstame algebrasgentle algebrastrivial extensionsBrauer graph algebrasadmissible cutsmarked Riemann surfacessymmetric special biserial algebras

Mathematics Subject Classification ID

Representation type (finite, tame, wild, etc.) of associative algebras (16G60) Representations of quivers and partially ordered sets (16G20) Representations of associative Artinian rings (16G10) Riemann surfaces; Weierstrass points; gap sequences (14H55) Cluster algebras (13F60)

Related Items (36)

Derived equivalence classification of Brauer graph algebras ⋮ Brauer graph algebras are closed under derived equivalence ⋮ Multiserial and special multiserial algebras and their representations ⋮ Auslander-Reiten components of symmetric special biserial algebras ⋮ A Geometric Model for the Module Category of a Gentle Algebra ⋮ The role of gentle algebras in higher homological algebra ⋮ Brauer configuration algebras: a generalization of Brauer graph algebras ⋮ Endomorphism algebras for a class of negative Calabi-Yau categories ⋮ On band modules and \(\tau \)-tilting finiteness ⋮ On the Lie algebra structure of the first Hochschild cohomology of gentle algebras and Brauer graph algebras ⋮ Derived categories of skew-gentle algebras and orbifolds ⋮ Mapping cones in the bounded derived category of a gentle algebra ⋮ The geometry of Brauer graph algebras and cluster mutations. ⋮ Universal deformation rings of modules for generalized Brauer tree algebras of polynomial growth ⋮ Dessins d'enfants, Brauer graph algebras and Galois invariants ⋮ Gerstenhaber algebra structure on the Hochschild cohomology of quadratic string algebras ⋮ A complete derived invariant for gentle algebras via winding numbers and Arf invariants ⋮ Exceptional sequences in the derived category of a gentle algebra ⋮ Almost Gentle Algebras and their Trivial Extensions ⋮ Classification of two-term tilting complexes over Brauer graph algebras ⋮ Special multiserial algebras are quotients of symmetric special multiserial algebras ⋮ Pairwise compatibility for 2-simple minded collections ⋮ Derived equivalences between symmetric special biserial algebras. ⋮ Cohen-Macaulay differential graded modules and negative Calabi-Yau configurations ⋮ On the non-periodic stable Auslander-Reiten Heller component for the Kronecker algebra over a complete discrete valuation ring ⋮ On stably biserial algebras and the Auslander-Reiten conjecture for special biserial algebras ⋮ Oriented flip graphs of polygonal subdivisions and noncrossing tree partitions ⋮ Special multiserial algebras, Brauer configuration algebras and more: A survey ⋮ A reduction theorem for \(\tau\)-rigid modules ⋮ Higher extensions for gentle algebras ⋮ Simplicial complexes and tilting theory for Brauer tree algebras ⋮ From Brauer graph algebras to biserial weighted surface algebras ⋮ Brauer Graph Algebras ⋮ Universal deformation rings of string modules over certain class of self-injective special biserial algebras ⋮ Weakly symmetric biserial algebras ⋮ On Auslander-Reiten components of string complexes for a certain class of symmetric special biserial algebras

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