Representation Theory and Beyond

ISBN-13: 9781470451318

Jan Šťovíček;Jan Trlifaj

Opis

It presents several themes of contemporary representation theory together with some new tools, such as stable ?-categories, stable derivators, and contramodules. In the first part, expanded lecture notes of four courses delivered at the workshop are presented, covering the representation theory of finite sets with correspondences, geometric theory of quiver Grassmannians, recent applications of contramodules to tilting theory, as well as symmetries in the representation theory over an abstract stable homotopy theory. The second part consists of six more-advanced papers based on plenary talks of the conference, presenting selected topics from contemporary representation theory: recollements and purity, maximal green sequences, cohomological Hall algebras, Hochschild cohomology of associative algebras, cohomology of local selfinjective algebras, and the higher Auslander-Reiten theory studied via homotopy theory.

Spis treści

• Workshop lecture notes: S. Bazzoni, Contramodules and their applications to tilting theory
• S. Bouc, Representations of finite sets and correspondences
• G. C. Irelli, Three lectures on quiver Grassmannians
• M. Rahn, Higher symmetries in abstract stable homotopy theories
• Conference proceedings papers: K. Erdmann, Cohomology of some local selfinjective algebras
• J. Franzen and M. Reineke, On the cohomological Hall algebra of the Kronecker quiver
• X. Fu and I. Herzog, The recollements of purity
• G. Jasso, Higher Auslander algebras of type $\mathbb$ and the higher Waldhausen $\mathsf$-constructions
• B. Keller and L. Demonet, A survey on maximal green sequences
• A. Solotar, The Gerstenhaber bracket in Hochschild cohomology: Methods and examples.