Tilting In Abelian Categories And Quasitilted Algebras

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Tilting in Abelian Categories and Quasitilted Algebras

Author : Dieter Happel
Publisher : American Mathematical Soc.
ISBN 13 : 0821804448
Total Pages : 88 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Tilting in Abelian Categories and Quasitilted Algebras by : Dieter Happel

Download or read book Tilting in Abelian Categories and Quasitilted Algebras written by Dieter Happel and published by American Mathematical Soc.. This book was released on 1996 with total page 88 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Idun Reiten
Publisher : American Mathematical Soc.
ISBN 13 : 9780821808504
Total Pages : 216 pages
Book Rating : 4.8/5 (85 download)

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Book Synopsis Algebras and Modules I by : Idun Reiten

Download or read book Algebras and Modules I written by Idun Reiten and published by American Mathematical Soc.. This book was released on 1998 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Abelian Groups and Modules

Author : Alberto Facchini
Publisher : Springer Science & Business Media
ISBN 13 : 9401104433
Total Pages : 521 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis Abelian Groups and Modules by : Alberto Facchini

Download or read book Abelian Groups and Modules written by Alberto Facchini and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Finite Dimensional Algebras and Related Topics

Author : V. Dlab
Publisher : Springer Science & Business Media
ISBN 13 : 9401715564
Total Pages : 392 pages
Book Rating : 4.4/5 (17 download)

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Book Synopsis Finite Dimensional Algebras and Related Topics by : V. Dlab

Download or read book Finite Dimensional Algebras and Related Topics written by V. Dlab and published by Springer Science & Business Media. This book was released on 2013-04-18 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Fla'vio Ulhoa Coelho
Publisher : CRC Press
ISBN 13 : 0429530013
Total Pages : 310 pages
Book Rating : 4.4/5 (295 download)

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Book Synopsis Representations of Algebras by : Fla'vio Ulhoa Coelho

Download or read book Representations of Algebras written by Fla'vio Ulhoa Coelho and published by CRC Press. This book was released on 2019-05-20 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Representations of Algebras, Geometry and Physics

Author : Kiyoshi Igusa
Publisher : American Mathematical Soc.
ISBN 13 : 1470452308
Total Pages : 241 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Representations of Algebras, Geometry and Physics by : Kiyoshi Igusa

Download or read book Representations of Algebras, Geometry and Physics written by Kiyoshi Igusa and published by American Mathematical Soc.. This book was released on 2021-05-17 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Handbook of Tilting Theory

Author : Lidia Angeleri Hügel
Publisher : Cambridge University Press
ISBN 13 : 9780521680455
Total Pages : 482 pages
Book Rating : 4.6/5 (84 download)

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Book Synopsis Handbook of Tilting Theory by : Lidia Angeleri Hügel

Download or read book Handbook of Tilting Theory written by Lidia Angeleri Hügel and published by Cambridge University Press. This book was released on 2007-01-04 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Andrzej Skowroński
Publisher : European Mathematical Society
ISBN 13 : 9783037190623
Total Pages : 732 pages
Book Rating : 4.1/5 (96 download)

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Book Synopsis Trends in Representation Theory of Algebras and Related Topics by : Andrzej Skowroński

Download or read book Trends in Representation Theory of Algebras and Related Topics written by Andrzej Skowroński and published by European Mathematical Society. This book was released on 2008 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 and Related Topics

Author : Andrzej Skowroński
Publisher : European Mathematical Society
ISBN 13 : 9783037191019
Total Pages : 744 pages
Book Rating : 4.1/5 (91 download)

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Book Synopsis Representations of Algebras and Related Topics by : Andrzej Skowroński

Download or read book Representations of Algebras and Related Topics written by Andrzej Skowroński and published by European Mathematical Society. This book was released on 2011 with total page 744 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : P. Dräxler
Publisher : Birkhäuser
ISBN 13 : 3034887167
Total Pages : 358 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Computational Methods for Representations of Groups and Algebras by : P. Dräxler

Download or read book Computational Methods for Representations of Groups and Algebras written by P. Dräxler and published by Birkhäuser. This book was released on 2012-12-06 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Algebras and Modules II

Author : Idun Reiten
Publisher : American Mathematical Soc.
ISBN 13 : 9780821810767
Total Pages : 596 pages
Book Rating : 4.8/5 (17 download)

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Book Synopsis Algebras and Modules II by : Idun Reiten

Download or read book Algebras and Modules II written by Idun Reiten and published by American Mathematical Soc.. This book was released on 1998 with total page 596 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Trends in the Representation Theory of Finite Dimensional Algebras

Author : Edward L. Green
Publisher : American Mathematical Soc.
ISBN 13 : 0821809288
Total Pages : 378 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Trends in the Representation Theory of Finite Dimensional Algebras by : Edward L. Green

Download or read book Trends in the Representation Theory of Finite Dimensional Algebras written by Edward L. Green and published by American Mathematical Soc.. This book was released on 1998 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 inspiration to researchers in related areas, as it includes original papers spanning a broad spectrum of representation theory.

Equivalence and Duality for Module Categories with Tilting and Cotilting for Rings

Author : Robert R. Colby
Publisher : Cambridge University Press
ISBN 13 : 9781139452434
Total Pages : 170 pages
Book Rating : 4.4/5 (524 download)

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Book Synopsis Equivalence and Duality for Module Categories with Tilting and Cotilting for Rings by : Robert R. Colby

Download or read book Equivalence and Duality for Module Categories with Tilting and Cotilting for Rings written by Robert R. Colby and published by Cambridge University Press. This book was released on 2004-03-22 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a unified approach to much of the theories of equivalence and duality between categories of modules that has transpired over the last 45 years. In particular, during the past dozen or so years many authors (including the authors of this book) have investigated relationships between categories of modules over a pair of rings that are induced by both covariant and contravariant representable functors, in particular by tilting and cotilting theories. By here collecting and unifying the basic results of these investigations with innovative and easily understandable proofs, the authors' aim is to provide an aid to further research in this central topic in abstract algebra, and a reference for all whose research lies in this field.

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

Author : Hagen Meltzer
Publisher : American Mathematical Soc.
ISBN 13 : 082183519X
Total Pages : 139 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Exceptional Vector Bundles, Tilting Sheaves and Tilting Complexes for Weighted Projective Lines by : Hagen Meltzer

Download or read book Exceptional Vector Bundles, Tilting Sheaves and Tilting Complexes for Weighted Projective Lines written by Hagen Meltzer and published by American Mathematical Soc.. This book was released on 2004 with total page 139 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Expository Lectures on Representation Theory

Author : Kiyoshi Igusa
Publisher : American Mathematical Soc.
ISBN 13 : 0821891405
Total Pages : 236 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Expository Lectures on Representation Theory by : Kiyoshi Igusa

Download or read book Expository Lectures on Representation Theory written by Kiyoshi Igusa and published by American Mathematical Soc.. This book was released on 2014-01-16 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Generalized Lie Theory in Mathematics, Physics and Beyond

Author : Sergei D. Silvestrov
Publisher : Springer Science & Business Media
ISBN 13 : 3540853324
Total Pages : 308 pages
Book Rating : 4.5/5 (48 download)

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Book Synopsis Generalized Lie Theory in Mathematics, Physics and Beyond by : Sergei D. Silvestrov

Download or read book Generalized Lie Theory in Mathematics, Physics and Beyond written by Sergei D. Silvestrov and published by Springer Science & Business Media. This book was released on 2008-11-18 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the cutting edge of the fundamental role of generalizations of Lie theory and related non-commutative and non-associative structures in mathematics and physics.

Trends in Representation Theory of Algebras and Related Topics

Author : José Antonio de la Peña
Publisher : American Mathematical Soc.
ISBN 13 : 0821838180
Total Pages : 282 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Trends in Representation Theory of Algebras and Related Topics by : José Antonio de la Peña

Download or read book Trends in Representation Theory of Algebras and Related Topics written by José Antonio de la Peña and published by American Mathematical Soc.. This book was released on 2006 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.