Representation Theory Of Algebras And Related Topics
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Representations of Algebras and Related Topics
Author: Andrzej Skowroński
language: en
Publisher: European Mathematical Society
Release Date: 2011
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.
Trends in Representation Theory of Algebras and Related Topics
Author: Andrzej Skowroński
language: en
Publisher: European Mathematical Society
Release Date: 2008
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, Poincare 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.
Representation Theory of Algebras and Related Topics
Author: Raymundo Bautista
language: en
Publisher: American Mathematical Soc.
Release Date: 1996
The 14 selected papers discuss recent thinking and findings on the representation theory of algebras and its interaction with other areas of mathematics such as algebraic geometry, ring theory, and the representation of groups. The topics include coils and multicoil algebras, representations of wild quivers, the Tits form of a tame algebra, almost split sequences and triangles for Artin algebras and orders, and using approximations to analyze the structure of representations. No index. Members of the Canadian Mathematical Society may order at the AMS member price of $57. Annotation copyright by Book News, Inc., Portland, OR