Triangulated Categories in the Representation of Finite Dimensional Algebras


Author: Dieter Happel
Publisher: Cambridge University Press
ISBN: 9780521339223
Category: Mathematics
Page: 208
View: 6704

An introduction to the use of triangulated categories in the study of representations of finite-dimensional algebras reveals that the derived categories are a useful tool in studying tilting processes.

Representations of Algebras and Related Topics


Author: Andrzej Skowroński,Kunio Yamagata
Publisher: European Mathematical Society
ISBN: 9783037191019
Category: Mathematics
Page: 728
View: 3688



Noncommutative Curves of Genus Zero

Related to Finite Dimensional Algebras
Author: Dirk Kussin
Publisher: American Mathematical Soc.
ISBN: 0821844008
Category: Mathematics
Page: 128
View: 9685

In these notes the author investigates noncommutative smooth projective curves of genus zero, also called exceptional curves. As a main result he shows that each such curve $\mathbb{X}$ admits, up to some weighting, a projective coordinate algebra which is a not necessarily commutative graded factorial domain $R$ in the sense of Chatters and Jordan. Moreover, there is a natural bijection between the points of $\mathbb{X}$ and the homogeneous prime ideals of height one in $R$, and these prime ideals are principal in a strong sense.

Surveys in Representation Theory of Algebras


Author: Alex Martsinkovsky,Kiyoshi Igusa,Gordana Todorov
Publisher: American Mathematical Soc.
ISBN: 1470436795
Category: Representations of algebras
Page: 203
View: 4809

This volume contains selected expository lectures delivered at the annual Maurice Auslander Distinguished Lectures and International Conference over the last several years. Reflecting the diverse landscape of modern representation theory of algebras, the selected articles include: a quick introduction to silting modules; a survey on the first decade of co-t-structures in triangulated categories; a functorial approach to the notion of module; a representation-theoretic approach to recollements in abelian categories; new examples of applications of relative homological algebra; connections between Coxeter groups and quiver representations; and recent progress on limits of approximation theory.

Trends in Representation Theory of Algebras and Related Topics


Author: Andrzej Skowroński
Publisher: European Mathematical Society
ISBN: 9783037190623
Category: Mathematics
Page: 710
View: 6184

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, combinatories, 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.

Handbook of Tilting Theory


Author: Dieter Happel,Henning Krause
Publisher: Cambridge University Press
ISBN: 9780521680455
Category: Mathematics
Page: 472
View: 4409

A handbook of key articles providing both an introduction and reference for newcomers and experts alike.

Expository Lectures on Representation Theory


Author: Kiyoshi Igusa, Alex Martsinkovsky, Gordana Todorov
Publisher: American Mathematical Soc.
ISBN: 0821891405
Category: Mathematics
Page: 224
View: 3879

This volume contains the proceedings of the Maurice Auslander Distinguished Lectures and International Conference, held April 25-30, 2012, in Falmouth, MA. The representation theory of finite dimensional algebras and related topics, especially cluster combinatorics, is a very active topic of research. This volume contains papers covering both the history and the latest developments in this topic. In particular, Otto Kerner gives a review of basic theorems and latest results about wild hereditary algebras, Yuri Berest develops the theory of derived representation schemes, and Markus Schmidmeier presents new applications of arc diagrams.

An Introduction to Quiver Representations


Author: Harm Derksen,Jerzy Weyman
Publisher: American Mathematical Soc.
ISBN: 1470425564
Category: Directed graphs
Page: 344
View: 1605

This book is an introduction to the representation theory of quivers and finite dimensional algebras. It gives a thorough and modern treatment of the algebraic approach based on Auslander-Reiten theory as well as the approach based on geometric invariant theory. The material in the opening chapters is developed starting slowly with topics such as homological algebra, Morita equivalence, and Gabriel's theorem. Next, the book presents Auslander-Reiten theory, including almost split sequences and the Auslander-Reiten transform, and gives a proof of Kac's generalization of Gabriel's theorem. Once this basic material is established, the book goes on with developing the geometric invariant theory of quiver representations. The book features the exposition of the saturation theorem for semi-invariants of quiver representations and its application to Littlewood-Richardson coefficients. In the final chapters, the book exposes tilting modules, exceptional sequences and a connection to cluster categories. The book is suitable for a graduate course in quiver representations and has numerous exercises and examples throughout the text. The book will also be of use to experts in such areas as representation theory, invariant theory and algebraic geometry, who want to learn about applications of quiver representations to their fields.

Representation Theory

A Homological Algebra Point of View
Author: Alexander Zimmermann
Publisher: Springer
ISBN: 3319079689
Category: Mathematics
Page: 707
View: 2715

Introducing the representation theory of groups and finite dimensional algebras, first studying basic non-commutative ring theory, this book covers the necessary background on elementary homological algebra and representations of groups up to block theory. It further discusses vertices, defect groups, Green and Brauer correspondences and Clifford theory. Whenever possible the statements are presented in a general setting for more general algebras, such as symmetric finite dimensional algebras over a field. Then, abelian and derived categories are introduced in detail and are used to explain stable module categories, as well as derived categories and their main invariants and links between them. Group theoretical applications of these theories are given – such as the structure of blocks of cyclic defect groups – whenever appropriate. Overall, many methods from the representation theory of algebras are introduced. Representation Theory assumes only the most basic knowledge of linear algebra, groups, rings and fields and guides the reader in the use of categorical equivalences in the representation theory of groups and algebras. As the book is based on lectures, it will be accessible to any graduate student in algebra and can be used for self-study as well as for classroom use.

London Mathematical Society lecture note series


Author: Boris I. Botvinnik
Publisher: N.A
ISBN: N.A
Category:
Page: N.A
View: 8660



London Mathematical Society lecture note series


Author: Michael S. Paterson
Publisher: N.A
ISBN: N.A
Category:
Page: N.A
View: 5094



The Legacy of Niels Henrik Abel

The Abel Bicentennial, Oslo, 2002
Author: Olav Arnfinn Laudal,Ragni Piene
Publisher: Springer Science & Business Media
ISBN: 3642189083
Category: Mathematics
Page: 784
View: 3206

A unique series of fascinating research papers on subjects related to the work of Niels Henrik Abel, written by some of the foremost specialists in their fields. Some of the authors have been specifically invited to present papers, discussing the influence of Abel in a mathematical-historical context. Others have submitted papers presented at the Abel Bicentennial Conference, Oslo June 3-8, 2002. The idea behind the book has been to produce a text covering a substantial part of the legacy of Abel, as perceived at the beginning of the 21st century.

London Mathematical Society lecture note series


Author: N.A
Publisher: N.A
ISBN: N.A
Category:
Page: N.A
View: 6152



London Mathematical Society lecture note series


Author: Michael Sh Braverman
Publisher: N.A
ISBN: N.A
Category:
Page: N.A
View: 1074



London Mathematical Society lecture note series


Author: E. Tournier
Publisher: N.A
ISBN: N.A
Category:
Page: N.A
View: 1827



London Mathematical Society lecture note series


Author: Nigel Ray,John Frank Adams,Grant Walker
Publisher: N.A
ISBN: N.A
Category:
Page: N.A
View: 9354



London Mathematical Society lecture note series


Author: Walter Schachermayer
Publisher: N.A
ISBN: N.A
Category:
Page: N.A
View: 3070



London Mathematical Society lecture note series


Author: S. K. Donaldson
Publisher: N.A
ISBN: N.A
Category: Mathematics
Page: N.A
View: 2468



London Mathematical Society lecture note series


Author: Manfred Stoll
Publisher: N.A
ISBN: N.A
Category:
Page: N.A
View: 3896



London Mathematical Society lecture note series


Author: Andrew Ranicki
Publisher: N.A
ISBN: N.A
Category:
Page: N.A
View: 456