scholarly journals Non-kissing and non-crossing complexes for locally gentle algebras

2019 ◽  
Vol 3 (4) ◽  
pp. 401-438 ◽  
Author(s):  
Yann Palu ◽  
Vincent Pilaud ◽  
Pierre-Guy Plamondon
Keyword(s):  
Gentle Algebras

Skewed-Gentle Algebras are Nodal

2015 ◽  
Vol 67 (4) ◽  
pp. 648-651
Author(s):  
V. V. Zembyk
Keyword(s):  
Gentle Algebras

Cohen–Macaulay Auslander algebras of skewed-gentle algebras

2016 ◽  
Vol 45 (2) ◽  
pp. 849-865
Author(s):  
Xinhong Chen ◽  
Ming Lu
Keyword(s):  
Gentle Algebras

scholarly journals Schemes of modules over gentle algebras and laminations of surfaces

2021 ◽  
Vol 28 (1) ◽  
Author(s):  
Christof Geiß ◽  
Daniel Labardini-Fragoso ◽  
Jan Schröer
Keyword(s):  
Special Class ◽  
Cluster Algebra ◽  
Irreducible Components ◽  
Gentle Algebras

AbstractWe study the affine schemes of modules over gentle algebras. We describe the smooth points of these schemes, and we also analyze their irreducible components in detail. Several of our results generalize formerly known results, e.g. by dropping acyclicity, and by incorporating band modules. A special class of gentle algebras are Jacobian algebras arising from triangulations of unpunctured marked surfaces. For these we obtain a bijection between the set of generically $$\tau $$ τ -reduced decorated irreducible components and the set of laminations of the surface. As an application, we get that the set of bangle functions (defined by Musiker–Schiffler–Williams) in the upper cluster algebra associated with the surface coincides with the set of generic Caldero-Chapoton functions (defined by Geiß–Leclerc–Schröer).

scholarly journals On the invariant theory for acyclic gentle algebras

2014 ◽  
Vol 367 (5) ◽  
pp. 3481-3508 ◽  
Author(s):  
Andrew T. Carroll ◽  
Calin Chindris
Keyword(s):  
Invariant Theory ◽  
Gentle Algebras

Gentle algebras are Gorenstein

2005 ◽  
pp. 129-133 ◽  
Author(s):  
Ch. Geiß ◽  
I. Reiten
Keyword(s):  
Gentle Algebras

scholarly journals Gentle algebras arising from surface triangulations

2010 ◽  
Vol 4 (2) ◽  
pp. 201-229 ◽  
Author(s):  
Ibrahim Assem ◽  
Thomas Brüstle ◽  
Gabrielle Charbonneau-Jodoin ◽  
Pierre-Guy Plamondon
Keyword(s):  
Gentle Algebras

scholarly journals Non-kissing complexes and tau-tilting for gentle algebras

2021 ◽  
Vol 274 (1343) ◽  
Author(s):  
Yann Palu ◽  
Vincent Pilaud ◽  
Pierre-Guy Plamondon
Keyword(s):  
Hasse Diagram ◽  
Uniform Lattice ◽  
Content Type ◽  
Gentle Algebras ◽  
Congruence Uniform ◽  
Kissing Complex ◽  
Tilting Complex

We interpret the support τ \tau -tilting complex of any gentle bound quiver as the non-kissing complex of walks on its blossoming quiver. Particularly relevant examples were previously studied for quivers defined by a subset of the grid or by a dissection of a polygon. We then focus on the case when the non-kissing complex is finite. We show that the graph of increasing flips on its facets is the Hasse diagram of a congruence-uniform lattice. Finally, we study its g \mathbf {g} -vector fan and prove that it is the normal fan of a non-kissing associahedron.

Semi-invariants of gentle algebras by deformation method and sphericity

2019 ◽  
Vol 528 ◽  
pp. 285-310
Author(s):  
D.A. Shmelkin
Keyword(s):  
Deformation Method ◽  
Gentle Algebras

scholarly journals Cohen–Macaulay Auslander algebras of gentle algebras

2019 ◽  
Vol 47 (9) ◽  
pp. 3597-3613
Author(s):  
Xinhong Chen ◽  
Ming Lu
Keyword(s):  
Gentle Algebras

scholarly journals Modules without Self-Extensions over Gentle Algebras

1999 ◽  
Vol 216 (1) ◽  
pp. 178-189 ◽  
Author(s):  
Jan Schröer
Keyword(s):  
Gentle Algebras
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