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Derived Equivalences For Group Rings
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Book Synopsis Derived Equivalences for Group Rings by : Steffen König
Download or read book Derived Equivalences for Group Rings written by Steffen König and published by Springer. This book was released on 2006-11-14 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained introduction is given to J. Rickard's Morita theory for derived module categories and its recent applications in representation theory of finite groups. In particular, Broué's conjecture is discussed, giving a structural explanation for relations between the p-modular character table of a finite group and that of its "p-local structure". The book is addressed to researchers or graduate students and can serve as material for a seminar. It surveys the current state of the field, and it also provides a "user's guide" to derived equivalences and tilting complexes. Results and proofs are presented in the generality needed for group theoretic applications.
Book Synopsis Derived Equivalences for Group Rings by : Steffen König
Download or read book Derived Equivalences for Group Rings written by Steffen König and published by . This book was released on 1998 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis The Block Theory of Finite Group Algebras: by : Markus Linckelmann
Download or read book The Block Theory of Finite Group Algebras: written by Markus Linckelmann and published by Cambridge University Press. This book was released on 2018-05-24 with total page 528 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a comprehensive introduction to the modular representation theory of finite groups, with an emphasis on block theory. The two volumes take into account classical results and concepts as well as some of the modern developments in the area. Volume 1 introduces the broader context, starting with general properties of finite group algebras over commutative rings, moving on to some basics in character theory and the structure theory of algebras over complete discrete valuation rings. In Volume 2, blocks of finite group algebras over complete p-local rings take centre stage, and many key results which have not appeared in a book before are treated in detail. In order to illustrate the wide range of techniques in block theory, the book concludes with chapters classifying the source algebras of blocks with cyclic and Klein four defect groups, and relating these classifications to the open conjectures that drive block theory.
Book Synopsis Homological Methods, Representation Theory, and Cluster Algebras by : Ibrahim Assem
Download or read book Homological Methods, Representation Theory, and Cluster Algebras written by Ibrahim Assem and published by Springer. This book was released on 2018-04-18 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents six mini-courses, all devoted to interactions between representation theory of algebras, homological algebra, and the new ever-expanding theory of cluster algebras. The interplay between the topics discussed in this text will continue to grow and this collection of courses stands as a partial testimony to this new development. The courses are useful for any mathematician who would like to learn more about this rapidly developing field; the primary aim is to engage graduate students and young researchers. Prerequisites include knowledge of some noncommutative algebra or homological algebra. Homological algebra has always been considered as one of the main tools in the study of finite-dimensional algebras. The strong relationship with cluster algebras is more recent and has quickly established itself as one of the important highlights of today’s mathematical landscape. This connection has been fruitful to both areas—representation theory provides a categorification of cluster algebras, while the study of cluster algebras provides representation theory with new objects of study. The six mini-courses comprising this text were delivered March 7–18, 2016 at a CIMPA (Centre International de Mathématiques Pures et Appliquées) research school held at the Universidad Nacional de Mar del Plata, Argentina. This research school was dedicated to the founder of the Argentinian research group in representation theory, M.I. Platzeck. The courses held were: Advanced homological algebra Introduction to the representation theory of algebras Auslander-Reiten theory for algebras of infinite representation type Cluster algebras arising from surfaces Cluster tilted algebras Cluster characters Introduction to K-theory Brauer graph algebras and applications to cluster algebras
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.
Book Synopsis Representations of Reductive Groups by : Roger W. Carter
Download or read book Representations of Reductive Groups written by Roger W. Carter and published by Cambridge University Press. This book was released on 1998-09-03 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume provides a very accessible introduction to the representation theory of reductive algebraic groups.
Book Synopsis Mathematisches Institut Georg-august-universität Göttingen, Seminars Summer Term 2004 by : Yuri Tschinkel
Download or read book Mathematisches Institut Georg-august-universität Göttingen, Seminars Summer Term 2004 written by Yuri Tschinkel and published by Universitätsverlag Göttingen. This book was released on 2004 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains lecture notes from the seminars [alpha]Number Theory", [alpha]Algebraic Geometry" and [alpha]Geometric methods in representation theory" which took place at the Mathematics Institute of the University of Göttingen during the Summer Term 2004. Most contributions report on recent work by the authors.
Author :Klaus W. Roggenkamp Publisher :Springer Science & Business Media ISBN 13 :9780792371137 Total Pages :488 pages Book Rating :4.3/5 (711 download)
Book Synopsis Algebra - Representation Theory by : Klaus W. Roggenkamp
Download or read book Algebra - Representation Theory written by Klaus W. Roggenkamp and published by Springer Science & Business Media. This book was released on 2001-08-31 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last three decades representation theory of groups, Lie algebras and associative algebras has undergone a rapid development through the powerful tool of almost split sequences and the Auslander-Reiten quiver. Further insight into the homology of finite groups has illuminated their representation theory. The study of Hopf algebras and non-commutative geometry is another new branch of representation theory which pushes the classical theory further. All this can only be seen in connection with an understanding of the structure of special classes of rings. The aim of this book is to introduce the reader to some modern developments in: Lie algebras, quantum groups, Hopf algebras and algebraic groups; non-commutative algebraic geometry; representation theory of finite groups and cohomology; the structure of special classes of rings.
Book Synopsis Structured Ring Spectra by : Andrew Baker
Download or read book Structured Ring Spectra written by Andrew Baker and published by Cambridge University Press. This book was released on 2004-11-18 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains some important new contributions to the theory of structured ring spectra.
Book Synopsis Modular Representation Theory of Finite Groups by : Michael John Collins
Download or read book Modular Representation Theory of Finite Groups written by Michael John Collins and published by Walter de Gruyter. This book was released on 2001 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.
Book Synopsis Geometric and Topological Aspects of the Representation Theory of Finite Groups by : Jon F. Carlson
Download or read book Geometric and Topological Aspects of the Representation Theory of Finite Groups written by Jon F. Carlson and published by Springer. This book was released on 2018-10-04 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: These proceedings comprise two workshops celebrating the accomplishments of David J. Benson on the occasion of his sixtieth birthday. The papers presented at the meetings were representative of the many mathematical subjects he has worked on, with an emphasis on group prepresentations and cohomology. The first workshop was titled "Groups, Representations, and Cohomology" and held from June 22 to June 27, 2015 at Sabhal Mòr Ostaig on the Isle of Skye, Scotland. The second was a combination of a summer school and workshop on the subject of "Geometric Methods in the Representation Theory of Finite Groups" and took place at the Pacific Institute for the Mathematical Sciences at the University of British Columbia in Vancouver from July 27 to August 5, 2016. The contents of the volume include a composite of both summer school material and workshop-derived survey articles on geometric and topological aspects of the representation theory of finite groups. The mission of the annually sponsored Summer Schools is to train and draw new students, and help Ph.D students transition to independent research.
Author :Representations of Algebraic Groups AMS-IMS-SIAM Joint Summer Research Conference, Quantum Groups Publisher :American Mathematical Soc. ISBN 13 :0821839241 Total Pages :270 pages Book Rating :4.8/5 (218 download)
Book Synopsis Representations of Algebraic Groups, Quantum Groups, and Lie Algebras by : Representations of Algebraic Groups AMS-IMS-SIAM Joint Summer Research Conference, Quantum Groups
Download or read book Representations of Algebraic Groups, Quantum Groups, and Lie Algebras written by Representations of Algebraic Groups AMS-IMS-SIAM Joint Summer Research Conference, Quantum Groups and published by American Mathematical Soc.. This book was released on 2006 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers various aspects of the representation theory of Lie algebras, finite groups of Lie types, Hecke algebras, and Lie super algebras. This book outlines connections among irreducible representations of certain blocks of reduced enveloping algebras of semi-simple Lie algebras in positive characteristic.
Book Synopsis Modular Representations of Finite Groups of Lie Type by : James E. Humphreys
Download or read book Modular Representations of Finite Groups of Lie Type written by James E. Humphreys and published by Cambridge University Press. This book was released on 2006 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive treatment of the representation theory of finite groups of Lie type over a field of the defining prime characteristic.
Book Synopsis Representation Theory by : Alexander Zimmermann
Download or read book Representation Theory written by Alexander Zimmermann and published by Springer. This book was released on 2014-08-15 with total page 707 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Blocks of Finite Groups and Their Invariants by : Benjamin Sambale
Download or read book Blocks of Finite Groups and Their Invariants written by Benjamin Sambale and published by Springer. This book was released on 2014-11-19 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing a nearly complete selection of up-to-date methods and results on block invariants with respect to their defect groups, this book covers the classical theory pioneered by Brauer, the modern theory of fusion systems introduced by Puig, the geometry of numbers developed by Minkowski, the classification of finite simple groups, and various computer assisted methods. In a powerful combination, these tools are applied to solve many special cases of famous open conjectures in the representation theory of finite groups. Most of the material is drawn from peer-reviewed journal articles, but there are also new previously unpublished results. In order to make the text self-contained, detailed proofs are given whenever possible. Several tables add to the text's usefulness as a reference. The book is aimed at experts in group theory or representation theory who may wish to make use of the presented ideas in their research.
Book Synopsis Functor Categories, Model Theory, Algebraic Analysis and Constructive Methods by : Alexander Martsinkovsky
Download or read book Functor Categories, Model Theory, Algebraic Analysis and Constructive Methods written by Alexander Martsinkovsky and published by Springer Nature. This book was released on with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Homological and Homotopical Aspects of Torsion Theories by : Apostolos Beligiannis
Download or read book Homological and Homotopical Aspects of Torsion Theories written by Apostolos Beligiannis and published by American Mathematical Soc.. This book was released on 2007 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper the authors investigate homological and homotopical aspects of a concept of torsion which is general enough to cover torsion and cotorsion pairs in abelian categories, $t$-structures and recollements in triangulated categories, and torsion pairs in stable categories. The proper conceptual framework for this study is the general setting of pretriangulated categories, an omnipresent class of additive categories which includes abelian, triangulated, stable, and more generally (homotopy categories of) closed model categories in the sense of Quillen, as special cases. The main focus of their study is on the investigation of the strong connections and the interplay between (co)torsion pairs and tilting theory in abelian, triangulated and stable categories on one hand, and universal cohomology theories induced by torsion pairs on the other hand. These new universal cohomology theories provide a natural generalization of the Tate-Vogel (co)homology theory. The authors also study the connections between torsion theories and closed model structures, which allow them to classify all cotorsion pairs in an abelian category and all torsion pairs in a stable category, in homotopical terms. For instance they obtain a classification of (co)tilting modules along these lines. Finally they give torsion theoretic applications to the structure of Gorenstein and Cohen-Macaulay categories, which provide a natural generalization of Gorenstein and Cohen-Macaulay rings.
