Triangulated Categories In The Representation Of Finite Dimensional Algebras
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Triangulated Categories In The Representation Theory Of Finite Dimensional Algebras
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Author : Dieter Happel
language : en
Publisher: Cambridge University Press
Release Date : 1988
Triangulated Categories In The Representation Theory Of Finite Dimensional Algebras written by Dieter Happel and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.
An introduction to the use of triangulated categories in the study of representations of finite-dimensional algebras.
Triangulated Categories In The Representation Of Finite Dimensional Algebras
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Author : Dieter Happel
language : en
Publisher:
Release Date : 1988
Triangulated Categories In The Representation Of Finite Dimensional Algebras written by Dieter Happel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Categories (Mathematics) categories.
Triangulated Categories In The Representation Theory Of Finite Dimensional Algebras
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Author : Dieter Happel
language : en
Publisher:
Release Date : 1988
Triangulated Categories In The Representation Theory Of Finite Dimensional Algebras written by Dieter Happel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Electronic books categories.
This book is an introduction to the use of triangulated categories in the study of representations of finite-dimensional algebras. In recent years representation theory has been an area of intense research and the author shows that derived categories of finite-dimensional algebras are a useful tool in studying tilting processes. Results on the structure of derived categories of hereditary algebras are used to investigate Dynkin algebras and interated tilted algebras. The author shows how triangulated categories arise naturally in the study of Frobenius categories. The study of trivial extension algebras and repetitive algebras is then developed using the triangulated structure on the stable category of the algebra's module category. With a comprehensive reference section, algebraists and research students in this field will find this an indispensable account of the theory of finite-dimensional algebras.
Handbook Of Tilting Theory
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Author : Lidia Angeleri Hügel
language : en
Publisher: Cambridge University Press
Release Date : 2007-01-04
Handbook Of Tilting Theory written by Lidia Angeleri Hügel and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-04 with Mathematics categories.
A handbook of key articles providing both an introduction and reference for newcomers and experts alike.
Representations Of Finite Dimensional Algebras And Related Topics In Lie Theory And Geometry
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Author : Vlastimil Dlab
language : en
Publisher: American Mathematical Soc.
Release Date :
Representations Of Finite Dimensional Algebras And Related Topics In Lie Theory And Geometry written by Vlastimil Dlab and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
These proceedings are from the Tenth International Conference on Representations of Algebras and Related Topics (ICRA X) held at The Fields Institute. In addition to the traditional ''instructional'' workshop preceding the conference, there were also workshops on ''Commutative Algebra, Algebraic Geometry and Representation Theory'', ''Finite Dimensional Algebras, Algebraic Groups and Lie Theory'', and ''Quantum Groups and Hall Algebras''. These workshops reflect the latest developments and the increasing interest in areas that are closely related to the representation theory of finite dimensional associative algebras. Although these workshops were organized separately, their topics are strongly interrelated. The workshop on Commutative Algebra, Algebraic Geometry and Representation Theory surveyed various recently established connections, such as those pertaining to the classification of vector bundles or Cohen-Macaulay modules over Noetherian rings, coherent sheaves on curves, or ideals in Weyl algebras. In addition, methods from algebraic geometry or commutative algebra relating to quiver representations and varieties of modules were presented. The workshop on Finite Dimensional Algebras, Algebraic Groups and Lie Theory surveyed developments in finite dimensional algebras and infinite dimensional Lie theory, especially as the two areas interact and may have future interactions. The workshop on Quantum Groups and Hall Algebras dealt with the different approaches of using the representation theory of quivers (and species) in order to construct quantum groups, working either over finite fields or over the complex numbers. In particular, these proceedings contain a quite detailed outline of the use of perverse sheaves in order to obtain canonical bases. The book is recommended for graduate students and researchers in algebra and geometry.
Triangulated Categories
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Author : Thorsten Holm
language : en
Publisher: Cambridge University Press
Release Date : 2010-06-24
Triangulated Categories written by Thorsten Holm and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-06-24 with Mathematics categories.
A 2010 collection of survey articles by leading experts covering fundamental aspects of triangulated categories, as well as applications in algebraic geometry, representation theory, commutative algebra, microlocal analysis and algebraic topology. This is a valuable reference for experts and a useful introduction for graduate students entering the field.
Representation Theory Of Finite Groups And Finite Dimensional Algebras
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Author : Michler
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Representation Theory Of Finite Groups And Finite Dimensional Algebras written by Michler and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
From April 1, 1984 until March 31, 1991 the Deutsche Forschungsgemeinschaft has sponsored the project "Representation Theory of Finite Groups and Finite Di mensional Algebras". The proposal for this project was submitted by B. Huppert (Mainz), B. Fischer (Bielefeld), G. Michler (Essen), H. Pahlings (Aachen) and C. M. Ringel (Bielefeld) in order to strengthen the interaction between the different re search areas in representation theory. The Deutsche Forschungsgemeinschaft has given many research positions and fellowships for young algebraists enabling them to do research at their own uni versities or as visitors at well known research institutions in America, Australia, England and France. The whole project benefitted very much from an extensive exchange programme between German and American scientists sponsored by the Deutsche Forschungsgemeinschaft and by the National Science Foundation of the United States. This volume presents lectures given in a final conference and reports by members of the project. It is divided into two parts. The first part contains seven survey articles describing recent advances in different areas of representation theory. These articles do not only concentrate on the work done by the German research groups, but also inform on major developments of the subject at all. The volume omits those topics already treated in book form. In particular, it does not contain a survey on K.
Representation Theory
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Author : Alexander Zimmermann
language : en
Publisher: Springer
Release Date : 2014-08-15
Representation Theory written by Alexander Zimmermann and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-15 with Mathematics categories.
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.
Representations Of Finite Dimensional Algebras
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Author : Peter Gabriel
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-09-12
Representations Of Finite Dimensional Algebras written by Peter Gabriel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-09-12 with Mathematics categories.
From the reviews: "... [Gabriel and Roiter] are pioneers in this subject and they have included proofs for statements which in their opinions are elementary, those which will help further understanding and those which are scarcely available elsewhere. They attempt to take us up to the point where we can find our way in the original literature. ..." --The Mathematical Gazette
Finite Dimensional Algebras And Related Topics
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Author : V. Dlab
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-18
Finite Dimensional Algebras And Related Topics written by V. Dlab and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-18 with Mathematics categories.
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.