Derived equivalence classification of Brauer graph algebras
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Publication:6363459
DOI10.1016/J.AIM.2022.108341zbMATH Open1516.16012arXiv2103.12049MaRDI QIDQ6363459
Alexandra Zvonareva, Sebastian Opper
Publication date: 22 March 2021
Abstract: We classify Brauer graph algebras up to derived equivalence by showing that the set of derived invariants introduced by Antipov is complete. These algebras first appeared in representation theory of finite groups and can be defined for any suitably decorated graph on an oriented surface. Motivated by the connection between Brauer graph algebras and gentle algebras we consider -trivial extensions of partially wrapped Fukaya categories associated to surfaces with boundary. This construction naturally enlarges the class of Brauer graph algebras and provides a way to construct derived equivalences between Brauer graph algebras with the same derived invariants. As part of the proof we provide an interpretation of derived invariants of Brauer graph algebras as orbit invariants of line fields under the action of the mapping class group.
Representations of quivers and partially ordered sets (16G20) Associative rings and algebras arising under various constructions (16S99) Derived categories and associative algebras (16E35)
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