Indecomposables in Derived Categories of Gentle Algebras

By Viktor Bekkert, H. Merklen. 2003

137 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/911cfcb578687dfca874fe9ef9b60aea5050b99b

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In Algebra and Number Theory

In Discrete Mathematics and Combinatorics

In Geometry and Topology

Citations in the corpus

A complete derived invariant for gentle algebras via winding numbers and Arf invariants (2019, unknown): “Their derived categories are well-understood [6, 13, 16, 17, 19, 20, 31].”
The almost split triangles for perfect complexes over gentle algebras (2009, background): “The following description of the indecomposable objects in K(Γ) was obtained in [8].”
Morphisms between indecomposable complexes in the bounded derived category of a gentle algebra (2014, methodology): “Recall from [8] that Λ(r, n,m) has no homotopy bands.”
A geometric model for the derived category of gentle algebras (2018, unknown): “e homotopy string and σ0σ1 ... is a right inﬁnite homotopy string. To each homotopy string and homotopy band σ as described above is associated a (possibly inﬁnite) complex of projective modules P• σ [8]. We now recall this construction. Deﬁnition 2.3 ([8]). (1) Let σ = σ1 ···σr be aﬁnite reducedhom”
Silting objects, simple-minded collections, $t$-structures and co-$t$-structures for finite-dimensional algebras (2012, unknown): “sable projective Λ-modules correspondingto the vertices 1 and 2. Thenup to isomorphismandup to shiftan indecomposable object in Db(modΛ) belongs to one of the following four families (see for example [19, 9]) · P1(n) = P1 → P1 → ... → P1 → P1, n ≥ 1, · R(n) = P1 → P1 → ... → P1 → P1 → P2, n ≥ 0, · L”
Flat surfaces and stability structures (2014, unknown): “In the special case when H0(F(S)) is the bounded derived category of a gentle algebra the classification of indecomposable objects was found by Drozd–Burban [16] and Bekkert–Merklen [8].”