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 complete derived invariant and silting theory for graded gentle algebras
4 Pith papers cite this work. Polarity classification is still indexing.
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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.
Necessary and sufficient conditions for complements to presilting objects in triangulated categories are established via co-t-structures, plus an equivalence characterizing silting-discrete algebras.
citing papers explorer
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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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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.
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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.
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Fishing for complements
Necessary and sufficient conditions for complements to presilting objects in triangulated categories are established via co-t-structures, plus an equivalence characterizing silting-discrete algebras.