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.
A geometric model for the derived category of gentle algebras
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Admissible fractional Brauer graph algebras admit easily checkable combinatorial invariants for derived equivalences and can be realized as repetitive algebras and r-fold trivial extensions of gentle algebras.
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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.
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Invariants of derived equivalences for admissible fractional Brauer graph algebras
Admissible fractional Brauer graph algebras admit easily checkable combinatorial invariants for derived equivalences and can be realized as repetitive algebras and r-fold trivial extensions of gentle algebras.