Exceptional Vector Bundles Tilting Sheaves And Tilting Complexes For Weighted Projective Lines
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Exceptional Vector Bundles, Tilting Sheaves and Tilting Complexes for Weighted Projective Lines
Author: Hagen Meltzer
language: en
Publisher: American Mathematical Soc.
Release Date: 2004
Deals with weighted projective lines, a class of non-commutative curves modelled by Geigle and Lenzing on a graded commutative sheaf theory. They play an important role in representation theory of finite-dimensional algebras; the complexity of the classification of coherent sheaves largely depends on the genus of these curves.
Representation Theory of Geigle-Lenzing Complete Intersections
Author: Martin Herschend
language: en
Publisher: American Mathematical Society
Release Date: 2023-05-23
View the abstract. https://www.ams.org/bookstore/pspdf/memo-285-1412-abstract.pdf?
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.