Biserial fractional Brauer graph algebras are tilting-discrete iff their reduced Brauer graph forms are, and tilting-discrete examples are closed under derived equivalence.
Skew-group $A_{\infty}$-categories as Fukaya categories of orbifolds
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abstract
We study the partially wrapped Fukaya category of a surface with boundary with an action of a group of order two. Inspired by skew-group algebras and categories, we define the notion of a skew-group $A_\infty$-category and let it play the role of the partially wrapped Fukaya category of an orbifold surface. We classify indecomposable objects in terms of graded curves with signs, or taggings, at orbifold points. We compute morphisms between a class of objects, and we use this to describe tilting objects and find algebras derived-equivalent to skew-gentle algebras.
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2026 1verdicts
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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.