This book, which explores recent trends in the representation theory of algebras and its exciting interaction with geometry, topology, commutative algebra, Lie algebras, combinatorics, quantum algebras, and theoretical field, is conceived as a handbook to provide easy access to the present state of knowledge and stimulate further development.

The many topics discussed include quivers, quivers with potential, bound quiver algebras, Jacobian algebras, cluster algebras and categories, Calabi-Yau algebras and categories, triangulated and derived categories, and quantum loop algebras.

This book consists of thirteen self-contained expository survey and research articles and is addressed to researchers and graduate students in algebra as well as a broader mathematical community. The articles contain a large number of examples and open problems and give new perspectives for research in the field.

A publication of the European Mathematical Society (EMS). Distributed within the Americas by the American Mathematical Society.

Readership

Graduate students and researchers interested in algebra and algebraic geometry.

Table of Contents

• C. Amiot -- On generalized cluster categories
• D. J. Benson, S. B. Iyengar, and H. Krause -- Module categories for finite group algebras
• B. Keller< -- On cluster theory and quantum dilogarithm identities
• B. Leclerc -- Quantum loop algebras, quiver varieties, and cluster algebras
• H. Lenzing -- Weighted projective lines and applications
• M. Linckelmann -- Cohomology of block algebras of finite groups
• P. Malicki and A. Skowroński -- Algebras with separating Auslander-Reiten components
• I. Mori -- Classification problems in noncommutative algebraic geometry and representation theory
• T. Nakanishi -- Periodicities in cluster algebras and dilogarithm identities
• J. A. de la Peña and A. Skowroński -- The Tits forms of tame algebras and their roots
• C. M. Ringel< -- The minimal representation-infinite algebras which are special biserial
• D. Simson -- Coalgebras of tame comodule type, comodule categories, and a tame-wild dichotomy problem
• G. Zwara -- Singularities of orbit closures in module varieties