# Trends in Representation Theory of Algebras and Related Topics

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*Andrzej Skowroński*

A publication of the European Mathematical Society

This book is concerned with recent trends in the representation theory
of algebras and its exciting interaction with geometry, topology, commutative
algebra, Lie algebras, quantum groups, homological algebra, invariant theory,
combinatorics, model theory and theoretical physics. The collection of
articles, written by leading researchers in the field, is conceived as a sort
of handbook providing easy access to the present state of knowledge and
stimulating further development.

The topics under discussion include diagram algebras, Brauer algebras,
cellular algebras, quasi-hereditary algebras, Hall algebras, Hecke
algebras, symplectic reflection algebras, Cherednik algebras,
Kashiwara crystals, Fock spaces, preprojective algebras, cluster
algebras, rank varieties, varieties of algebras and modules, moduli of
representations of quivers, semi-invariants of quivers,
Cohen–Macaulay modules, singularities, coherent sheaves, derived
categories, spectral representation theory, Coxeter polynomials,
Auslander–Reiten theory, Calabi–Yau triangulated
categories, Poincaré duality spaces, selfinjective algebras,
periodic algebras, stable module categories, Hochschild cohomologies,
deformations of algebras, Galois coverings of algebras, tilting
theory, algebras of small homological dimensions, representation types
of algebras, and model theory.

This book consists of fifteen self-contained expository survey articles and is
addressed to researchers and graduate students in algebra as well as a broader
mathematical community. They contain a large number of 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 research mathematicians interested in representation theory.