Homological invariants of the arrow removal operation

Abstract: Several homological conjectures in representation theory are related with specific problems concerning the homological behaviour and the structure theory of finite dimensional algebras. In joint work with Edward Green and Oyvind Solberg we developed new reduction techniques (vertex removal operation and arrow removal operation) on quotients of path algebras for testing the finiteness of the finitistic dimension. In this talk, we will review these operations and we will focus on the arrow removal operation. In particular, we will show that Gorensteinness, singularity categories and the finite generation condition Fg for the Hochschild cohomology are invariants under the arrow removal operation for a finite dimensional algebra. This is joint work with Karin Erdmann and Oyvind Solberg.

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

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