Classification of two-term tilting complexes over Brauer graph algebras

Abstract

Using only the combinatorics of its defining ribbon graph, we classify the two-term tilting complexes, as well as their indecomposable summands, of a Brauer graph algebra. As an application, we determine precisely the class of Brauer graph algebras which are tilting-discrete.

Revised version. To appear in Math. Z

References in corpus (3)

• Silting mutation in triangulated categories
• Topological aspects of completely integrable foliations
• Classifying tilting complexes over preprojective algebras of Dynkin type

Cited by in corpus (11)

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• Derived equivalence classification of Brauer graph algebras
• Report on the finiteness of silting objects
• Tame block algebras of Hecke algebras of classical type
• Complete gentle and special biserial algebras are $g$-tame
• On $\tau$-tilting finiteness of symmetric algebras of polynomial growth
• $\tau$-tilting finiteness of two-point algebras II
• On $\tau$-tilting modules over trivial extensions of gentle tree algebras