An Introduction To Kac Moody Groups Over Fields

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An Introduction to Kac–Moody Groups Over Fields

Timothée Marquis
An Introduction to Kac Moody Groups Over Fields Book PDF

Author : Timothée Marquis
Publisher : Unknown
Page : 331 pages
File Size : 45,5 Mb
Release : 2018
Category : MATHEMATICS
ISBN : 3037196874

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An Introduction to Kac–Moody Groups Over Fields by Timothée Marquis Pdf

The interest for Kac–Moody algebras and groups has grown exponentially in the past decades, both in the mathematical and physics communities, and with it also the need for an introductory textbook on the topic. The aims of this book are twofold: - to offer an accessible, reader-friendly and self-contained introduction to Kac–Moody algebras and groups; - to clean the foundations and to provide a unified treatment of the theory. The book starts with an outline of the classical Lie theory, used to set the scene. Part II provides a self-contained introduction to Kac–Moody algebras. The heart of the book is Part III, which develops an intuitive approach to the construction and fundamental properties of Kac–Moody groups. It is complemented by two appendices, respectively offering introductions to affine group schemes and to the theory of buildings. Many exercises are included, accompanying the readers throughout their journey. The book assumes only a minimal background in linear algebra and basic topology, and is addressed to anyone interested in learning about Kac–Moody algebras and/or groups, from graduate (master) students to specialists.

Lie Algebras of Finite and Affine Type

Roger William Carter
Lie Algebras of Finite and Affine Type Book PDF

Author : Roger William Carter
Publisher : Cambridge University Press
Page : 662 pages
File Size : 49,8 Mb
Release : 2005-10-27
Category : Mathematics
ISBN : 0521851386

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Lie Algebras of Finite and Affine Type by Roger William Carter Pdf

This book provides a thorough but relaxed mathematical treatment of Lie algebras.

Kac-Moody Groups, their Flag Varieties and Representation Theory

Shrawan Kumar
Kac Moody Groups their Flag Varieties and Representation Theory Book PDF

Author : Shrawan Kumar
Publisher : Springer Science & Business Media
Page : 613 pages
File Size : 45,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461201052

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Kac-Moody Groups, their Flag Varieties and Representation Theory by Shrawan Kumar Pdf

Kac-Moody Lie algebras 9 were introduced in the mid-1960s independently by V. Kac and R. Moody, generalizing the finite-dimensional semisimple Lie alge bras which we refer to as the finite case. The theory has undergone tremendous developments in various directions and connections with diverse areas abound, including mathematical physics, so much so that this theory has become a stan dard tool in mathematics. A detailed treatment of the Lie algebra aspect of the theory can be found in V. Kac's book [Kac-90l This self-contained work treats the algebro-geometric and the topological aspects of Kac-Moody theory from scratch. The emphasis is on the study of the Kac-Moody groups 9 and their flag varieties XY, including their detailed construction, and their applications to the representation theory of g. In the finite case, 9 is nothing but a semisimple Y simply-connected algebraic group and X is the flag variety 9 /Py for a parabolic subgroup p y C g.

"Abstract'' Homomorphisms of Split Kac-Moody Groups

Pierre-Emmanuel Caprace
Abstract Homomorphisms of Split Kac Moody Groups Book PDF

Author : Pierre-Emmanuel Caprace
Publisher : American Mathematical Soc.
Page : 84 pages
File Size : 42,5 Mb
Release : 2009-03-06
Category : Mathematics
ISBN : 9780821842584

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"Abstract'' Homomorphisms of Split Kac-Moody Groups by Pierre-Emmanuel Caprace Pdf

This work is devoted to the isomorphism problem for split Kac-Moody groups over arbitrary fields. This problem turns out to be a special case of a more general problem, which consists in determining homomorphisms of isotropic semisimple algebraic groups to Kac-Moody groups, whose image is bounded. Since Kac-Moody groups possess natural actions on twin buildings, and since their bounded subgroups can be characterized by fixed point properties for these actions, the latter is actually a rigidity problem for algebraic group actions on twin buildings. The author establishes some partial rigidity results, which we use to prove an isomorphism theorem for Kac-Moody groups over arbitrary fields of cardinality at least $4$. In particular, he obtains a detailed description of automorphisms of Kac-Moody groups. This provides a complete understanding of the structure of the automorphism group of Kac-Moody groups over ground fields of characteristic $0$. The same arguments allow to treat unitary forms of complex Kac-Moody groups. In particular, the author shows that the Hausdorff topology that these groups carry is an invariant of the abstract group structure. Finally, the author proves the non-existence of cocentral homomorphisms of Kac-Moody groups of indefinite type over infinite fields with finite-dimensional target. This provides a partial solution to the linearity problem for Kac-Moody groups.

Geometry of Matrices

Zhexian Wan,Luogeng Hua
Geometry of Matrices Book PDF

Author : Zhexian Wan,Luogeng Hua
Publisher : World Scientific
Page : 396 pages
File Size : 47,8 Mb
Release : 1996
Category : Mathematics
ISBN : 9810226381

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Geometry of Matrices by Zhexian Wan,Luogeng Hua Pdf

The present monograph is a state-of-art survey of the geometry of matrices whose study was initiated by L K Hua in the forties. The geometry of rectangular matrices, of alternate matrices, of symmetric matrices, and of hermitian matrices over a division ring or a field are studied in detail. The author's recent results on geometry of symmetric matrices and of hermitian matrices are included. A chapter on linear algebra over a division ring and one on affine and projective geometry over a division ring are also included. The book is clearly written so that graduate students and third or fourth year undergraduate students in mathematics can read it without difficulty.

Introduction to Quantum Groups

George Lusztig
Introduction to Quantum Groups Book PDF

Author : George Lusztig
Publisher : Springer Science & Business Media
Page : 361 pages
File Size : 42,9 Mb
Release : 2010-10-27
Category : Mathematics
ISBN : 9780817647179

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Introduction to Quantum Groups by George Lusztig Pdf

The quantum groups discussed in this book are the quantized enveloping algebras introduced by Drinfeld and Jimbo in 1985, or variations thereof. The theory of quantum groups has led to a new, extremely rigid structure, in which the objects of the theory are provided with canonical basis with rather remarkable properties. This book will be of interest to mathematicians working in the representation theory of Lie groups and Lie algebras, knot theorists and to theoretical physicists and graduate students. Since large parts of the book are independent of the theory of perverse sheaves, the book could also be used as a text book.

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 : 55,7 Mb
Release : 2016-04-26
Category : Mathematics
ISBN : 9780128046838

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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

Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification

Jacob Greenstein,David Hernandez,Kailash C. Misra,Prasad Senesi
Interactions of Quantum Affine Algebras with Cluster Algebras Current Algebras and Categorification Book PDF

Author : Jacob Greenstein,David Hernandez,Kailash C. Misra,Prasad Senesi
Publisher : Springer Nature
Page : 453 pages
File Size : 50,7 Mb
Release : 2022-03-11
Category : Mathematics
ISBN : 9783030638498

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Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification by Jacob Greenstein,David Hernandez,Kailash C. Misra,Prasad Senesi Pdf

This volume collects chapters that examine representation theory as connected with affine Lie algebras and their quantum analogues, in celebration of the impact Vyjayanthi Chari has had on this area. The opening chapters are based on mini-courses given at the conference “Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification”, held on the occasion of Chari’s 60th birthday at the Catholic University of America in Washington D.C., June 2018. The chapters that follow present a broad view of the area, featuring surveys, original research, and an overview of Vyjayanthi Chari’s significant contributions. Written by distinguished experts in representation theory, a range of topics are covered, including: String diagrams and categorification Quantum affine algebras and cluster algebras Steinberg groups for Jordan pairs Dynamical quantum determinants and Pfaffians Interactions of Quantum Affine Algebras with Cluster Algebras, Current Algebras and Categorification will be an ideal resource for researchers in the fields of representation theory and mathematical physics.

Recent Advances in Representation Theory, Quantum Groups, Algebraic Geometry, and Related Topics

Pramod M. Achar,Dijana Jakelić,Kailash C. Misra,Milen Yakimov
Recent Advances in Representation Theory Quantum Groups Algebraic Geometry and Related Topics Book PDF

Author : Pramod M. Achar,Dijana Jakelić,Kailash C. Misra,Milen Yakimov
Publisher : American Mathematical Society
Page : 296 pages
File Size : 49,8 Mb
Release : 2014-08-27
Category : Mathematics
ISBN : 9780821898529

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Recent Advances in Representation Theory, Quantum Groups, Algebraic Geometry, and Related Topics by Pramod M. Achar,Dijana Jakelić,Kailash C. Misra,Milen Yakimov Pdf

This volume contains the proceedings of two AMS Special Sessions "Geometric and Algebraic Aspects of Representation Theory" and "Quantum Groups and Noncommutative Algebraic Geometry" held October 13–14, 2012, at Tulane University, New Orleans, Louisiana. Included in this volume are original research and some survey articles on various aspects of representations of algebras including Kac—Moody algebras, Lie superalgebras, quantum groups, toroidal algebras, Leibniz algebras and their connections with other areas of mathematics and mathematical physics.

Rigidity in Dynamics and Geometry

Marc Burger,Alessandra Iozzi
Rigidity in Dynamics and Geometry Book PDF

Author : Marc Burger,Alessandra Iozzi
Publisher : Springer Science & Business Media
Page : 494 pages
File Size : 47,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9783662047439

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Rigidity in Dynamics and Geometry by Marc Burger,Alessandra Iozzi Pdf

This volume of proceedings is an offspring of the special semester Ergodic Theory, Geometric Rigidity and Number Theory which was held at the Isaac Newton Institute for Mathematical Sciences in Cambridge, UK, from Jan uary until July, 2000. Beside the activities during the semester, there were workshops held in January, March and July, the first being of introductory nature with five short courses delivered over a week. Although the quality of the workshops was excellent throughout the semester, the idea of these proceedings came about during the March workshop, which is hence more prominently represented, The format of the volume has undergone many changes, but what has remained untouched is the enthusiasm of the contributors since the onset of the project: suffice it to say that even though only two months elapsed between the time we contacted the potential authors and the deadline to submit the papers, the deadline was respected in the vast majority of the cases. The scope of the papers is not completely uniform throughout the volume, although there are some points in common. We asked the authors to write papers keeping in mind the idea that they should be accessible to students. At the same time, we wanted the papers not to be a summary of results that appeared somewhere else.

Langlands Correspondence for Loop Groups

Edward Frenkel
Langlands Correspondence for Loop Groups Book PDF

Author : Edward Frenkel
Publisher : Cambridge University Press
Page : 5 pages
File Size : 46,5 Mb
Release : 2007-06-28
Category : Mathematics
ISBN : 9780521854436

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Langlands Correspondence for Loop Groups by Edward Frenkel Pdf

The first account of local geometric Langlands Correspondence, a new area of mathematical physics developed by the author.

Symmetries, Integrable Systems and Representations

Kenji Iohara,Sophie Morier-Genoud,Bertrand Rémy
Symmetries Integrable Systems and Representations Book PDF

Author : Kenji Iohara,Sophie Morier-Genoud,Bertrand Rémy
Publisher : Springer Science & Business Media
Page : 633 pages
File Size : 46,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781447148630

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Symmetries, Integrable Systems and Representations by Kenji Iohara,Sophie Morier-Genoud,Bertrand Rémy Pdf

This volume is the result of two international workshops; Infinite Analysis 11 – Frontier of Integrability – held at University of Tokyo, Japan in July 25th to 29th, 2011, and Symmetries, Integrable Systems and Representations held at Université Claude Bernard Lyon 1, France in December 13th to 16th, 2011. Included are research articles based on the talks presented at the workshops, latest results obtained thereafter, and some review articles. The subjects discussed range across diverse areas such as algebraic geometry, combinatorics, differential equations, integrable systems, representation theory, solvable lattice models and special functions. Through these topics, the reader will find some recent developments in the field of mathematical physics and their interactions with several other domains.

Groups, Graphs and Random Walks

Tullio Ceccherini-Silberstein,Maura Salvatori,Ecaterina Sava-Huss
Groups Graphs and Random Walks Book PDF

Author : Tullio Ceccherini-Silberstein,Maura Salvatori,Ecaterina Sava-Huss
Publisher : Cambridge University Press
Page : 539 pages
File Size : 47,8 Mb
Release : 2017-06-29
Category : Mathematics
ISBN : 9781316604403

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Groups, Graphs and Random Walks by Tullio Ceccherini-Silberstein,Maura Salvatori,Ecaterina Sava-Huss Pdf

An up-to-date, panoramic account of the theory of random walks on groups and graphs, outlining connections with various mathematical fields.

Lattice Quantum Field Theory Of The Dirac And Gauge Fields: Selected Topics

Belal Ehsan Baaquie
Lattice Quantum Field Theory Of The Dirac And Gauge Fields Selected Topics Book PDF

Author : Belal Ehsan Baaquie
Publisher : World Scientific
Page : 317 pages
File Size : 48,7 Mb
Release : 2020-07-30
Category : Science
ISBN : 9789811209710

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Lattice Quantum Field Theory Of The Dirac And Gauge Fields: Selected Topics by Belal Ehsan Baaquie Pdf

Quantum Chromodynamics is the theory of strong interactions: a quantum field theory of colored gluons (Yang-Mills gauge fields) coupled to quarks (Dirac fermion fields). Lattice gauge theory is defined by discretizing spacetime into a four-dimensional lattice — and entails defining gauge fields and Dirac fermions on a lattice. The applications of lattice gauge theory are vast, from the study of high-energy theory and phenomenology to the numerical studies of quantum fields.Lattice Quantum Field Theory of the Dirac and Gauge Fields: Selected Topics examines the mathematical foundations of lattice gauge theory from first principles. It is indispensable for the study of Dirac and lattice gauge fields and lays the foundation for more advanced and specialized studies.

Nonassociative Algebras And Related Topics - Proceedings Of The International Symposium

K Yamaguti,N Kawamoto
Nonassociative Algebras And Related Topics Proceedings Of The International Symposium Book PDF

Author : K Yamaguti,N Kawamoto
Publisher : World Scientific
Page : 382 pages
File Size : 40,5 Mb
Release : 1991-11-29
Category : Electronic
ISBN : 9789814556200

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Nonassociative Algebras And Related Topics - Proceedings Of The International Symposium by K Yamaguti,N Kawamoto Pdf

The rapid progress in genomics and related technologies has increased interest in genetically modified organisms (GMOs). This concise and highly readable book equips the reader with essential information about what genes are, how they work, and how they can be modified and used in biotechnology. The book starts with a summary of the beginnings of life, the structure and components of living organisms, and an outline of genetic engineering.The coverage of human genetics spans race, human evolution and migration, the sex chromosomes, gene therapy, and forensic science. A separate chapter is devoted to the genetics and evolution of some of the major disease-causing organisms. On environmental genetics, the book considers the risks of releasing agricultural GM plants, as well as bioremediation and metal extraction by GM plants. Applications of genetic modification in agriculture — pest-resistant plants, herbicide resistance, and improved foods — are presented as part of a discussion on sustainable agriculture to emphasize the role played by GM plants in relation to chemicals, analytic techniques, and organic farming.