Tilting In Abelian Categories And Quasitilted Algebras

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Tilting in Abelian Categories and Quasitilted Algebras

Dieter Happel,Idun Reiten,Sverre O. Smalø
Tilting in Abelian Categories and Quasitilted Algebras Book PDF

Author : Dieter Happel,Idun Reiten,Sverre O. Smalø
Publisher : American Mathematical Soc.
Page : 88 pages
File Size : 48,8 Mb
Release : 1996
Category : Mathematics
ISBN : 9780821804445

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Tilting in Abelian Categories and Quasitilted Algebras by Dieter Happel,Idun Reiten,Sverre O. Smalø Pdf

In this book, the authors generalize with respect to a tilting module of projective dimension at most one for an artin algebra to tilting with respect to a torsion pair in an abelian category. A general theory is developed for such tilting and the reader is led to a generalization for tilted algebras which the authors call ``quasitilted algebras''. This class also contains the canonical algebras, and the authors show that the quasitilted algebras are characterized by having global dimension at most two and each indecomposable module having projective dimension at most one or injective dimension at most one. The authors also give other characterizations of quasitilted algebras and give methods for constructing such algebras. In particular, they investigate when one-point extensions of hereditary algebras are quasitilted.

Algebras and Modules I

Idun Reiten,Sverre O. Smalø,Øyvind Solberg,Canadian Mathematical Society
Algebras and Modules I Book PDF

Author : Idun Reiten,Sverre O. Smalø,Øyvind Solberg,Canadian Mathematical Society
Publisher : American Mathematical Soc.
Page : 216 pages
File Size : 46,8 Mb
Release : 1998
Category : Mathematics
ISBN : 0821808508

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Algebras and Modules I by Idun Reiten,Sverre O. Smalø,Øyvind Solberg,Canadian Mathematical Society Pdf

Surveys developments in the representation theory of finite dimensional algebras and related topics in seven papers illustrating different techniques developed over the recent years. For graduate students and researchers with a background in commutative algebra, including rings, modules, and homological algebra. Suitable as a text for an advanced graduate course. No index. Member prices are $31 for institutions and $23 for individuals, and are available to members of the Canadian Mathematical Society. Annotation copyrighted by Book News, Inc., Portland, OR

Finite Dimensional Algebras and Related Topics

V. Dlab,Leonard Scott
Finite Dimensional Algebras and Related Topics Book PDF

Author : V. Dlab,Leonard Scott
Publisher : Springer Science & Business Media
Page : 392 pages
File Size : 46,6 Mb
Release : 2013-04-18
Category : Mathematics
ISBN : 9789401715560

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Finite Dimensional Algebras and Related Topics by V. Dlab,Leonard Scott Pdf

Based on invited lectures at the 1992 Canadian Algebra Seminar, this volume represents an up-to-date and unique report on finite-dimensional algebras as a subject with many serious interactions with other mathematical disciplines, including algebraic groups and Lie theory, automorphic forms, sheaf theory, finite groups, and homological algebra. It will interest mathematicians and graduate students in these and related subjects as an introduction to research in an area of increasing relevance and importance.

Representations of Algebras

Fla'vio Ulhoa Coelho,Hector Goldschimdt
Representations of Algebras Book PDF

Author : Fla'vio Ulhoa Coelho,Hector Goldschimdt
Publisher : CRC Press
Page : 310 pages
File Size : 52,7 Mb
Release : 2019-05-20
Category : Mathematics
ISBN : 9780429530012

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Representations of Algebras by Fla'vio Ulhoa Coelho,Hector Goldschimdt Pdf

This volume contains the proceedings of the Conference on Representations of Algebras - Sao Paulo (CRASP), held at the Instituto de Matematica e Estatistica of the Universidade de Sao Paulo, Brazil. It discusses Hopf, tubular, quasischurian, wild hereditary, concealed-canonical Artin, Brauer star, and Koszul algebras.

Abelian Groups and Modules

Alberto Facchini,Claudia Menini
Abelian Groups and Modules Book PDF

Author : Alberto Facchini,Claudia Menini
Publisher : Springer Science & Business Media
Page : 521 pages
File Size : 49,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789401104432

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Abelian Groups and Modules by Alberto Facchini,Claudia Menini Pdf

On the 26th of November 1992 the organizing committee gathered together, at Luigi Salce's invitation, for the first time. The tradition of abelian groups and modules Italian conferences (Rome 77, Udine 85, Bressanone 90) needed to be kept up by one more meeting. Since that first time it was clear to us that our goal was not so easy. In fact the main intended topics of abelian groups, modules over commutative rings and non commutative rings have become so specialized in the last years that it looked really ambitious to fit them into only one meeting. Anyway, since everyone of us shared the same mathematical roots, we did want to emphasize a common link. So we elaborated the long symposium schedule: three days of abelian groups and three days of modules over non commutative rings with a two days' bridge of commutative algebra in between. Many of the most famous names in these fields took part to the meeting. Over 140 participants, both attending and contributing the 18 Main Lectures and 64 Communications (see list on page xv) provided a really wide audience for an Algebra meeting. Now that the meeting is over, we can say that our initial feeling was right.

Handbook of Tilting Theory

Lidia Angeleri Hügel,Dieter Happel,Henning Krause
Handbook of Tilting Theory Book PDF

Author : Lidia Angeleri Hügel,Dieter Happel,Henning Krause
Publisher : Cambridge University Press
Page : 482 pages
File Size : 41,6 Mb
Release : 2007-01-04
Category : Mathematics
ISBN : 052168045X

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Handbook of Tilting Theory by Lidia Angeleri Hügel,Dieter Happel,Henning Krause Pdf

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

Trends in Representation Theory of Algebras and Related Topics

Andrzej Skowroński
Trends in Representation Theory of Algebras and Related Topics Book PDF

Author : Andrzej Skowroński
Publisher : European Mathematical Society
Page : 732 pages
File Size : 43,5 Mb
Release : 2008
Category : Representations of algebras
ISBN : 3037190620

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Trends in Representation Theory of Algebras and Related Topics by Andrzej Skowroński Pdf

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.

Representations of Algebras, Geometry and Physics

Kiyoshi Igusa,Alex Martsinkovsky,Gordana Todorov
Representations of Algebras Geometry and Physics Book PDF

Author : Kiyoshi Igusa,Alex Martsinkovsky,Gordana Todorov
Publisher : American Mathematical Soc.
Page : 241 pages
File Size : 49,7 Mb
Release : 2021-05-17
Category : Education
ISBN : 9781470452308

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Representations of Algebras, Geometry and Physics by Kiyoshi Igusa,Alex Martsinkovsky,Gordana Todorov Pdf

This volume contains selected expository lectures delivered at the 2018 Maurice Auslander Distinguished Lectures and International Conference, held April 25–30, 2018, at the Woods Hole Oceanographic Institute, Woods Hole, MA. Reflecting recent developments in modern representation theory of algebras, the selected topics include an introduction to a new class of quiver algebras on surfaces, called “geodesic ghor algebras”, a detailed presentation of Feynman categories from a representation-theoretic viewpoint, connections between representations of quivers and the structure theory of Coxeter groups, powerful new applications of approximable triangulated categories, new results on the heart of a t t-structure, and an introduction to methods of constructive category theory.

Representations of Algebras and Related Topics

Andrzej Skowroński,Kunio Yamagata
Representations of Algebras and Related Topics Book PDF

Author : Andrzej Skowroński,Kunio Yamagata
Publisher : European Mathematical Society
Page : 744 pages
File Size : 40,6 Mb
Release : 2011
Category : Algebra
ISBN : 3037191015

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Representations of Algebras and Related Topics by Andrzej Skowroński,Kunio Yamagata Pdf

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.

Computational Methods for Representations of Groups and Algebras

P. Dräxler,G. Michler,C.M. Ringel
Computational Methods for Representations of Groups and Algebras Book PDF

Author : P. Dräxler,G. Michler,C.M. Ringel
Publisher : Birkhäuser
Page : 358 pages
File Size : 46,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034887168

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Computational Methods for Representations of Groups and Algebras by P. Dräxler,G. Michler,C.M. Ringel Pdf

This book presents material from 3 survey lectures and 14 additional invited lectures given at the Euroconference "Computational Methods for Representations of Groups and Algebras" held at Essen University in April 1997. The purpose of this meeting was to provide a survey of general theoretical and computational methods and recent advances in the representation theory of groups and algebras. The foundations of these research areas were laid in survey articles by P. Dräxler and R. Nörenberg on "Classification problems in the representation theory of finite-dimensional algebras", R. A. Wilson on "Construction of finite matrix groups" and E. Green on "Noncommutative Gröbner bases, and projective resolutions". Furthermore, new applications of the computational methods in linear algebra to the revision of the classification of finite simple sporadic groups are presented. Computational tools (including high-performance computations on supercomputers) have become increasingly important for classification problems. They are also inevitable for the construction of projective resolutions of finitely generated modules over finite-dimensional algebras and the study of group cohomology and rings of invariants. A major part of this book is devoted to a survey of algorithms for computing special examples in the study of Grothendieck groups, quadratic forms and derived categories of finite-dimensional algebras. Open questions on Lie algebras, Bruhat orders, Coxeter groups and Kazhdan Lusztig polynomials are investigated with the aid of computer programs. The contents of this book provide an overview on the present state of the art. Therefore it will be very useful for graduate students and researchers in mathematics, computer science and physics.

Trends in the Representation Theory of Finite Dimensional Algebras

Edward L. Green,Birge Huisgen-Zimmermann
Trends in the Representation Theory of Finite Dimensional Algebras Book PDF

Author : Edward L. Green,Birge Huisgen-Zimmermann
Publisher : American Mathematical Soc.
Page : 356 pages
File Size : 40,7 Mb
Release : 1998
Category : Mathematics
ISBN : 9780821809280

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Trends in the Representation Theory of Finite Dimensional Algebras by Edward L. Green,Birge Huisgen-Zimmermann Pdf

This refereed collection of research papers and survey articles reflects the interplay of finite-dimensional algebras with other areas (algebraic geometry, homological algebra, and the theory of quantum groups). Current trends are presented from the discussions at the AMS-IMS-SIAM Joint Summer Research Conference at the University of Washington (Seattle). The volume features several excellent expository articles which will introduce the beginning researcher to cutting-edge topics in representation theory. The book will also provide inspiration to researchers in related areas, as it includes original papers spanning a broad spectrum of representation theory. It's features include: work outlining significant progress on long-standing open problems; survey articles offering both overviews and introductions to various subfields of the topic; and, expositions reflecting the interplay between the representation theory of algebras and other fields.

Algebras and Modules II

Idun Reiten,Sverre O. Smalø,Øyvind Solberg,Canadian Mathematical Society
Algebras and Modules II Book PDF

Author : Idun Reiten,Sverre O. Smalø,Øyvind Solberg,Canadian Mathematical Society
Publisher : American Mathematical Soc.
Page : 596 pages
File Size : 43,5 Mb
Release : 1998
Category : Mathematics
ISBN : 0821810766

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Algebras and Modules II by Idun Reiten,Sverre O. Smalø,Øyvind Solberg,Canadian Mathematical Society Pdf

The 43 research papers demonstrate the application of recent developments in the representation theory of artin algebras and related topics. Among the algebras considered are tame, bi- serial, cellular, factorial hereditary, Hopf, Koszul, non- polynomial growth, pre-projective, Termperley-Lieb, tilted, and quasi-tilted. Other topics include tilting and co-tilting modules and generalizations as *-modules, exceptional sequences of modules and vector bundles, homological conjectives, and vector space categories. The treatment assumes knowledge of non- commutative algebra, including rings, modules, and homological algebra at a graduate or professional level. No index. Member prices are $79 for institutions and $59 for individuals, which also apply to members of the Canadian Mathematical Society. Annotation copyrighted by Book News, Inc., Portland, OR

Exceptional Vector Bundles, Tilting Sheaves and Tilting Complexes for Weighted Projective Lines

Hagen Meltzer,Richard D. Canary,Darryl McCullough
Exceptional Vector Bundles Tilting Sheaves and Tilting Complexes for Weighted Projective Lines Book PDF

Author : Hagen Meltzer,Richard D. Canary,Darryl McCullough
Publisher : American Mathematical Soc.
Page : 139 pages
File Size : 48,5 Mb
Release : 2004
Category : Mathematics
ISBN : 9780821835197

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Exceptional Vector Bundles, Tilting Sheaves and Tilting Complexes for Weighted Projective Lines by Hagen Meltzer,Richard D. Canary,Darryl McCullough Pdf

This work 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. We study exceptional vector bundles on weighted projective lines and show in particular that the braid group acts transitively on the set of complete exceptional sequences of such bundles. We further investigate tilting sheaves on weighted projective lines and determine the Auslander-Reiten components of modules over their endomorphism rings. Finally we study tilting complexes in the derived category and present detailed classification results in the case of weighted projective lines of hyperelliptic type.

Trends in Representation Theory of Algebras and Related Topics

José Antonio de la Peña,Raymundo Bautista
Trends in Representation Theory of Algebras and Related Topics Book PDF

Author : José Antonio de la Peña,Raymundo Bautista
Publisher : American Mathematical Soc.
Page : 282 pages
File Size : 44,9 Mb
Release : 2006
Category : Representations of algebras
ISBN : 9780821838181

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Trends in Representation Theory of Algebras and Related Topics by José Antonio de la Peña,Raymundo Bautista Pdf

This book is based on lectures given during a Workshop on Representations of Algebras and Related Topics. Some additional articles are included in order to complete a panoramic view of the main trends of the subject. The volume contains original presentations by leading algebraists addressed to specialists as well as to a broader mathematical audience. The articles include new proofs, examples, and detailed arguments. Topics under discussion include moduli spaces associated to quivers, canonical basis of quantum algebras, categorifications and derived categories, $A$-infinity algebras and functor categories, cluster algebras, support varieties for modules and complexes, the Gabriel-Roiter measure for modules, and selfinjective algebras.

Expository Lectures on Representation Theory

Kiyoshi Igusa, Alex Martsinkovsky, Gordana Todorov
Expository Lectures on Representation Theory Book PDF

Author : Kiyoshi Igusa, Alex Martsinkovsky, Gordana Todorov
Publisher : American Mathematical Soc.
Page : 236 pages
File Size : 51,6 Mb
Release : 2014-01-16
Category : Mathematics
ISBN : 9780821891407

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Expository Lectures on Representation Theory by Kiyoshi Igusa, Alex Martsinkovsky, Gordana Todorov Pdf

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.