Quotients of extriangulated categories by hereditary-type subcategories are quasi-abelian, and abelian precisely when the subcategory is cluster tilting in a relative extriangulated structure.
A geometric model for the derived category of gentle algebras
5 Pith papers cite this work. Polarity classification is still indexing.
5
Pith papers citing it
fields
math.RT 5verdicts
UNVERDICTED 5representative citing papers
Skew-group A_∞-categories are defined to represent Fukaya categories of orbifolds, with indecomposable objects classified as graded curves with taggings and tilting objects yielding derived equivalences to skew-gentle algebras.
Gives a combinatorial realization of the Auslander-Reiten correspondence between resolving subcategories and tilting modules for gentle tree algebras.
Biserial fractional Brauer graph algebras are tilting-discrete iff their reduced Brauer graph forms are, and tilting-discrete examples are closed under derived equivalence.
Admissible fractional Brauer graph algebras admit easily checkable combinatorial invariants of derived equivalence and arise as repetitive algebras and r-fold trivial extensions of gentle algebras.
citing papers explorer
-
Quasi-abelian quotients in extriangulated categories
Quotients of extriangulated categories by hereditary-type subcategories are quasi-abelian, and abelian precisely when the subcategory is cluster tilting in a relative extriangulated structure.
-
Skew-group $A_{\infty}$-categories as Fukaya categories of orbifolds
Skew-group A_∞-categories are defined to represent Fukaya categories of orbifolds, with indecomposable objects classified as graded curves with taggings and tilting objects yielding derived equivalences to skew-gentle algebras.
-
Resolving subcategories for gentle algebras III: Tilting modules for gentle tree algebras
Gives a combinatorial realization of the Auslander-Reiten correspondence between resolving subcategories and tilting modules for gentle tree algebras.
-
Two-term tilting complexes of biserial fractional Brauer graph algebras
Biserial fractional Brauer graph algebras are tilting-discrete iff their reduced Brauer graph forms are, and tilting-discrete examples are closed under derived equivalence.
-
Invariants of derived equivalences for admissible fractional Brauer graph algebras
Admissible fractional Brauer graph algebras admit easily checkable combinatorial invariants of derived equivalence and arise as repetitive algebras and r-fold trivial extensions of gentle algebras.