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A complete derived invariant and silting theory for graded gentle algebras
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We confirm a conjecture by Lekili and Polishchuk that the geometric invariants which they construct for homologically smooth graded (not necessarily proper) gentle algebras form a complete derived invariant. Hence, we obtain a complete invariant of triangle equivalences for partially wrapped Fukaya categories of graded surfaces with stops. A key ingredient of the proof is the full description of homologically smooth graded gentle algebras whose perfect derived categories admit silting objects. We also apply this to classify which graded gentle algebras admit pre-silting objects that are not partial silting. In particular, this allows us to construct a family of counterexamples to the question whether any pre-silting object in the derived category of a finite-dimensional algebra is partial silting.
Forward citations
Cited by 2 Pith papers
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Hochschild Cohomology of the Symmetric Square of an Annulus with Stops
The symmetric square dg algebra of an annulus with stops is non-formal for n1≥2, with a nontrivial m3, and its Hochschild cohomology is computed explicitly in all cases.
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The 1-periodic derived category of a gentle algebra : Part 1 -- Indecomposable objects
For a gentle algebra, indecomposables in the 1-periodic derived category are exactly string objects from curves between marked points and band objects from primitive closed curves with indecomposable k[x,x^-1]-modules.
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