Derived equivalence classification of Brauer graph algebras

Abstract: In this talk, I will explain the classification of Brauer graph algebras up to derived equivalence. These algebras first appeared in representation theory of finite groups and can be defined for any suitably decorated graph on an oriented surface. The classification relies on the connection between Brauer graph algebras and gentle algebras and the classification of the mapping class group orbits of the homotopy classes of line fields on surfaces. We consider A-infinity 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. This is based on joint work with Sebastian Opper.

mathematical physicscommutative algebraalgebraic geometryrings and algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

( slides | video )

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Longitudinal Algebra and Geometry Open ONline Seminar (LAGOON)

Series comments: Description: Research webinar series

The LAGOON webinar series was supported as part of the International Centre for Mathematical Sciences (ICMS) and the Isaac Newton Institute for Mathematical Sciences (INI) Online Mathematical Sciences Seminars and is now sponsored by the University of Cologne and the University of Pavia. Please register here to obtain the Zoom link and password for the meetings.

LAGOON will take place online every last Wednesday of the month from 14:00-15:00 (Time Zone Berlin, Rome, Paris).

Videos of the talks can be viewed here.

Video recordings of past talks until April 2022 can still be viewed on the ICMS webpage here.

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