Derived Picard groups of representation-finite symmetric algebras

Abstract: I will talk about my work on computing the derived Picard groups of a particular class of symmetric representation-finite algebras of type D. We obtain an explicit description of these groups via generators and relations. In particular, we prove that these groups are generated by spherical twists along a collection of 0-spherical objects, the shift and, roughly speaking, outer automorphisms of the algebras. One of the key ingredients in the proof is the faithfulness of braid group actions by spherical twists along ADE configurations of 0-spherical objects. Another part of the strategy is based on the fact that symmetric representation-finite algebras are tilting-connected. To apply this result we in particular develop a combinatorial-geometric model for silting mutations in type D, generalising the classical concepts of Brauer trees and Kauer moves. I will also discuss possible directions in which the result might be extended to a more general categorical context.

mathematical physicscommutative algebraalgebraic geometryrings and algebrasrepresentation theorysymplectic geometry

Audience: researchers in the topic

( slides )

Comments: Meeting Link

uni-koeln.zoom.us/j/91875528987?pwd=TjNZV1lNdVJNOWUrR2xNalRuQWk3dz09

Meeting ID: 918 7552 8987 Password: LAGOON2022

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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).

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