Abstract
We complete a derived equivalence classification of the gentle two-cycle algebras initiated in earlier papers by Avella-Alaminos and Bobinski–Malicki.
Highlights
Introduction and the Main ResultThroughout the paper k denotes a fixed algebraically closed field
For a algebra one considers its derived category Db( ), which has a structure of a triangulated category
Derived categories appearing in representation theory of algebras have connections with derived categories studied in algebraic geometry
Summary
Throughout the paper k denotes a fixed algebraically closed field. For a (finite-dimensional basic connected) algebra one considers its (bounded) derived category Db( ), which has a structure of a triangulated category. Derived categories appearing in representation theory of algebras have connections with derived categories studied in algebraic geometry (see for example [11, 24, 31]). These categories serve as a source for constructions of categorifications of cluster algebras (this line of research was initiated by a fundamental paper by Buan, Marsh, Reineke, Reiten and Todorov [20]) and have links to theoretical physics (including famous Orlov’s theorem [36]). A study of derived categories (in particular derived equivalences) in the representation theory of algebras was initiated by papers of Happel [28, Presented by Henning Krause
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