Representations Of Finite Dimensional Algebras And Related Topics In Lie Theory And Geometry

Representations Of Finite Dimensional Algebras And Related Topics In Lie Theory And Geometry Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Representations Of Finite Dimensional Algebras And Related Topics In Lie Theory And Geometry book. This book definitely worth reading, it is an incredibly well-written.

Representations of Finite Dimensional Algebras and Related Topics in Lie Theory and Geometry

Vlastimil Dlab,Claus Michael Ringel
Representations of Finite Dimensional Algebras and Related Topics in Lie Theory and Geometry Book PDF

Author : Vlastimil Dlab,Claus Michael Ringel
Publisher : American Mathematical Soc.
Page : 502 pages
File Size : 53,5 Mb
Release : 2004
Category : Associative algebras
ISBN : 9780821834169

Get Book

Representations of Finite Dimensional Algebras and Related Topics in Lie Theory and Geometry by Vlastimil Dlab,Claus Michael Ringel Pdf

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.

Representations of Finite Dimensional Algebras and Related Topics in Lie Theory and Geometry

Vlastimil Dlab,Claus Michael Ringel
Representations of Finite Dimensional Algebras and Related Topics in Lie Theory and Geometry Book PDF

Author : Vlastimil Dlab,Claus Michael Ringel
Publisher : American Mathematical Soc.
Page : 508 pages
File Size : 46,6 Mb
Release : 2024-06-01
Category : Mathematics
ISBN : 0821871455

Get Book

Representations of Finite Dimensional Algebras and Related Topics in Lie Theory and Geometry by Vlastimil Dlab,Claus Michael Ringel Pdf

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.

Lie Theory

Jean-Philippe Anker,Bent Orsted
Lie Theory Book PDF

Author : Jean-Philippe Anker,Bent Orsted
Publisher : Springer Science & Business Media
Page : 331 pages
File Size : 47,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9780817681920

Get Book

Lie Theory by Jean-Philippe Anker,Bent Orsted Pdf

* First of three independent, self-contained volumes under the general title, "Lie Theory," featuring original results and survey work from renowned mathematicians. * Contains J. C. Jantzen's "Nilpotent Orbits in Representation Theory," and K.-H. Neeb's "Infinite Dimensional Groups and their Representations." * Comprehensive treatments of the relevant geometry of orbits in Lie algebras, or their duals, and the correspondence to representations. * Should benefit graduate students and researchers in mathematics and mathematical physics.

Representations of Algebras and Related Topics

Ragnar-Olaf Buchweitz,Helmut Lenzing
Representations of Algebras and Related Topics Book PDF

Author : Ragnar-Olaf Buchweitz,Helmut Lenzing
Publisher : American Mathematical Soc.
Page : 420 pages
File Size : 46,9 Mb
Release : 2024-06-01
Category : Mathematics
ISBN : 0821885928

Get Book

Representations of Algebras and Related Topics by Ragnar-Olaf Buchweitz,Helmut Lenzing Pdf

This proceedings volume resulted from the Tenth International Conference on Representations of Algebras and Related Topics held at The Fields Institute (Toronto, ON, Canada). The collection of research and survey articles, honoring Vlastimil Dlab's seventieth birthday, reflects state-of-the-art research on the topic. Leading experts contributed papers, demonstrating the interaction between representation theory of finite dimensional algebras and neighboring subjects. A wide range of topics are covered, including quantum groups, the theory of Lie algebras, the geometry and combinatorics of tilting theory, commutative algebra, algebraic geometry, homology theories, and derived and triangulated categories. The book is suitable for graduate students and researchers interested in the theory of algebras.

Introduction to Finite and Infinite Dimensional Lie (Super)algebras

Neelacanta Sthanumoorthy
Introduction to Finite and Infinite Dimensional Lie Super algebras Book PDF

Author : Neelacanta Sthanumoorthy
Publisher : Academic Press
Page : 512 pages
File Size : 44,7 Mb
Release : 2016-04-26
Category : Mathematics
ISBN : 9780128046838

Get Book

Introduction to Finite and Infinite Dimensional Lie (Super)algebras by Neelacanta Sthanumoorthy Pdf

Lie superalgebras are a natural generalization of Lie algebras, having applications in geometry, number theory, gauge field theory, and string theory. Introduction to Finite and Infinite Dimensional Lie Algebras and Superalgebras introduces the theory of Lie superalgebras, their algebras, and their representations. The material covered ranges from basic definitions of Lie groups to the classification of finite-dimensional representations of semi-simple Lie algebras. While discussing all classes of finite and infinite dimensional Lie algebras and Lie superalgebras in terms of their different classes of root systems, the book focuses on Kac-Moody algebras. With numerous exercises and worked examples, it is ideal for graduate courses on Lie groups and Lie algebras. Discusses the fundamental structure and all root relationships of Lie algebras and Lie superalgebras and their finite and infinite dimensional representation theory Closely describes BKM Lie superalgebras, their different classes of imaginary root systems, their complete classifications, root-supermultiplicities, and related combinatorial identities Includes numerous tables of the properties of individual Lie algebras and Lie superalgebras Focuses on Kac-Moody algebras

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 : 47,9 Mb
Release : 2011
Category : Algebra
ISBN : 3037191015

Get Book

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.

Geometric Representation Theory and Extended Affine Lie Algebras

Erhard Neher,Alistair Savage,Weiqiang Wang
Geometric Representation Theory and Extended Affine Lie Algebras Book PDF

Author : Erhard Neher,Alistair Savage,Weiqiang Wang
Publisher : American Mathematical Soc.
Page : 226 pages
File Size : 42,7 Mb
Release : 2011
Category : Nonassociative rings
ISBN : 9780821852378

Get Book

Geometric Representation Theory and Extended Affine Lie Algebras by Erhard Neher,Alistair Savage,Weiqiang Wang Pdf

Lie theory has connections to many other disciplines such as geometry, number theory, mathematical physics, and algebraic combinatorics. The interaction between algebra, geometry and combinatorics has proven to be extremely powerful in shedding new light on each of these areas. This book presents the lectures given at the Fields Institute Summer School on Geometric Representation Theory and Extended Affine Lie Algebras held at the University of Ottawa in 2009. It provides a systematic account by experts of some of the exciting developments in Lie algebras and representation theory in the last two decades. It includes topics such as geometric realizations of irreducible representations in three different approaches, combinatorics and geometry of canonical and crystal bases, finite $W$-algebras arising as the quantization of the transversal slice to a nilpotent orbit, structure theory of extended affine Lie algebras, and representation theory of affine Lie algebras at level zero. This book will be of interest to mathematicians working in Lie algebras and to graduate students interested in learning the basic ideas of some very active research directions. The extensive references in the book will be helpful to guide non-experts to the original sources.

Lie Algebras and Related Topics

Georgia Benkart
Lie Algebras and Related Topics Book PDF

Author : Georgia Benkart
Publisher : American Mathematical Soc.
Page : 313 pages
File Size : 41,6 Mb
Release : 1990
Category : Mathematics
ISBN : 9780821851197

Get Book

Lie Algebras and Related Topics by Georgia Benkart Pdf

The 1984 classification of the finite-dimensional restricted simple Lie algebras over an algebraically closed field of characteristic $p>7$ provided the impetus for a Special Year of Lie Algebras, held at the University of Wisconsin, Madison, during 1987-88. Work done during the Special Year and afterward put researchers much closer toward a solution of the long-standing problem of determining the finite-dimensional simple Lie algebras over an algebraically closed field of characteristic $p>7$. This volume contains the proceedings of a conference on Lie algebras and related topics, held in May 1988 to mark the end of the Special Year. The conference featured lectures on Lie algebras of prime characteristic, algebraic groups, combinatorics and representation theory, and Kac-Moody and Virasoro algebras. Many facets of recent research on Lie theory are reflected in the papers presented here, testifying to the richness and diversity of this topic.

Lie Algebras and Related Topics

Daniel J. Britten,Frank W. Lemire,R. V. Moody
Lie Algebras and Related Topics Book PDF

Author : Daniel J. Britten,Frank W. Lemire,R. V. Moody
Publisher : American Mathematical Soc.
Page : 398 pages
File Size : 49,9 Mb
Release : 1986
Category : Mathematics
ISBN : 0821860097

Get Book

Lie Algebras and Related Topics by Daniel J. Britten,Frank W. Lemire,R. V. Moody Pdf

As the Proceedings of the 1984 Canadian Mathematical Society's Summer Seminar, this book focuses on some advances in the theory of semisimple Lie algebras and some direct outgrowths of that theory. The following papers are of particular interest: an important survey article by R. Block and R. Wilson on restricted simple Lie algebras, a survey of universal enveloping algebras of semisimple Lie algebras by W. Borho, a course on Kac-Moody Lie algebras by I. G. Macdonald with an extensive bibliography of this field by Georgia Benkart, and a course on formal groups by M. Hazewinkel. Because of the expository surveys and courses, the book will be especially useful to graduate students in Lie theory, as well as to researchers in the field.

Lie Algebras, Lie Superalgebras, Vertex Algebras and Related Topics

Kailash C. Misra,Daniel K. Nakano,Brian J. Parshall
Lie Algebras Lie Superalgebras Vertex Algebras and Related Topics Book PDF

Author : Kailash C. Misra,Daniel K. Nakano,Brian J. Parshall
Publisher : American Mathematical Soc.
Page : 355 pages
File Size : 52,6 Mb
Release : 2016-06-28
Category : Group theory and generalizations
ISBN : 9781470418441

Get Book

Lie Algebras, Lie Superalgebras, Vertex Algebras and Related Topics by Kailash C. Misra,Daniel K. Nakano,Brian J. Parshall Pdf

This book contains the proceedings of the 2012–2014 Southeastern Lie Theory Workshop Series held at North Carolina State University in April 2012, at College of Charleston in December 2012, at Louisiana State University in May 2013, and at University of Georgia in May 2014. Some of the articles by experts in the field survey recent developments while others include new results in representations of Lie algebras, and quantum groups, vertex (operator) algebras and Lie superalgebras.

Introduction to Representation Theory

Pavel I. Etingof,Oleg Golberg,Sebastian Hensel ,Tiankai Liu ,Alex Schwendner ,Dmitry Vaintrob ,Elena Yudovina
Introduction to Representation Theory Book PDF

Author : Pavel I. Etingof,Oleg Golberg,Sebastian Hensel ,Tiankai Liu ,Alex Schwendner ,Dmitry Vaintrob ,Elena Yudovina
Publisher : American Mathematical Soc.
Page : 228 pages
File Size : 41,8 Mb
Release : 2011
Category : Mathematics
ISBN : 9780821853511

Get Book

Introduction to Representation Theory by Pavel I. Etingof,Oleg Golberg,Sebastian Hensel ,Tiankai Liu ,Alex Schwendner ,Dmitry Vaintrob ,Elena Yudovina Pdf

Very roughly speaking, representation theory studies symmetry in linear spaces. It is a beautiful mathematical subject which has many applications, ranging from number theory and combinatorics to geometry, probability theory, quantum mechanics, and quantum field theory. The goal of this book is to give a ``holistic'' introduction to representation theory, presenting it as a unified subject which studies representations of associative algebras and treating the representation theories of groups, Lie algebras, and quivers as special cases. Using this approach, the book covers a number of standard topics in the representation theories of these structures. Theoretical material in the book is supplemented by many problems and exercises which touch upon a lot of additional topics; the more difficult exercises are provided with hints. The book is designed as a textbook for advanced undergraduate and beginning graduate students. It should be accessible to students with a strong background in linear algebra and a basic knowledge of abstract algebra.

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 : 54,9 Mb
Release : 2008
Category : Representations of algebras
ISBN : 3037190620

Get Book

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.

Perspectives in Lie Theory

Filippo Callegaro,Giovanna Carnovale,Fabrizio Caselli,Corrado De Concini,Alberto De Sole
Perspectives in Lie Theory Book PDF

Author : Filippo Callegaro,Giovanna Carnovale,Fabrizio Caselli,Corrado De Concini,Alberto De Sole
Publisher : Springer
Page : 461 pages
File Size : 54,8 Mb
Release : 2017-12-07
Category : Mathematics
ISBN : 9783319589718

Get Book

Perspectives in Lie Theory by Filippo Callegaro,Giovanna Carnovale,Fabrizio Caselli,Corrado De Concini,Alberto De Sole Pdf

Lie theory is a mathematical framework for encoding the concept of symmetries of a problem, and was the central theme of an INdAM intensive research period at the Centro de Giorgi in Pisa, Italy, in the academic year 2014-2015. This book gathers the key outcomes of this period, addressing topics such as: structure and representation theory of vertex algebras, Lie algebras and superalgebras, as well as hyperplane arrangements with different approaches, ranging from geometry and topology to combinatorics.

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 : 45,7 Mb
Release : 2013-04-18
Category : Mathematics
ISBN : 9789401715560

Get Book

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.

Structure and Geometry of Lie Groups

Joachim Hilgert,Karl-Hermann Neeb
Structure and Geometry of Lie Groups Book PDF

Author : Joachim Hilgert,Karl-Hermann Neeb
Publisher : Springer Science & Business Media
Page : 742 pages
File Size : 42,7 Mb
Release : 2011-11-06
Category : Mathematics
ISBN : 9780387847948

Get Book

Structure and Geometry of Lie Groups by Joachim Hilgert,Karl-Hermann Neeb Pdf

This self-contained text is an excellent introduction to Lie groups and their actions on manifolds. The authors start with an elementary discussion of matrix groups, followed by chapters devoted to the basic structure and representation theory of finite dimensinal Lie algebras. They then turn to global issues, demonstrating the key issue of the interplay between differential geometry and Lie theory. Special emphasis is placed on homogeneous spaces and invariant geometric structures. The last section of the book is dedicated to the structure theory of Lie groups. Particularly, they focus on maximal compact subgroups, dense subgroups, complex structures, and linearity. This text is accessible to a broad range of mathematicians and graduate students; it will be useful both as a graduate textbook and as a research reference.