Lie Groups Number Theory And Vertex Algebras
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Lie Groups Number Theory And Vertex Algebras
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Author : Dražen Adamović
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-05-10
Lie Groups Number Theory And Vertex Algebras written by Dražen Adamović 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 2021-05-10 with Education categories.
This volume contains the proceedings of the conference Representation Theory XVI, held from June 25–29, 2019, in Dubrovnik, Croatia. The articles in the volume address selected aspects of representation theory of reductive Lie groups and vertex algebras, and are written by prominent experts in the field as well as junior researchers. The three main topics of these articles are Lie theory, number theory, and vertex algebras.
Lie Groups Number Theory And Vertex Algebras
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Author : Dražen Adamović
language : en
Publisher:
Release Date : 2021
Lie Groups Number Theory And Vertex Algebras written by Dražen Adamović and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with Representations of algebras categories.
Lie Algebras Vertex Operator Algebras And Their Applications
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Author : Yi-Zhi Huang
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Lie Algebras Vertex Operator Algebras And Their Applications written by Yi-Zhi Huang 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 2007 with Mathematics categories.
The articles in this book are based on talks given at the international conference 'Lie algebras, vertex operator algebras and their applications'. The focus of the papers is mainly on Lie algebras, quantum groups, vertex operator algebras and their applications to number theory, combinatorics and conformal field theory.
Introduction To Vertex Operator Algebras And Their Representations
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Author : James Lepowsky
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Introduction To Vertex Operator Algebras And Their Representations written by James Lepowsky 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 2012-12-06 with Mathematics categories.
* Introduces the fundamental theory of vertex operator algebras and its basic techniques and examples. * Begins with a detailed presentation of the theoretical foundations and proceeds to a range of applications. * Includes a number of new, original results and brings fresh perspective to important works of many other researchers in algebra, lie theory, representation theory, string theory, quantum field theory, and other areas of math and physics.
Lie Algebras Vertex Operator Algebras And Related Topics
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Author : Katrina Barron
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-08-15
Lie Algebras Vertex Operator Algebras And Related Topics written by Katrina Barron 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 2017-08-15 with Mathematics categories.
This volume contains the proceedings of the conference on Lie Algebras, Vertex Operator Algebras, and Related Topics, celebrating the 70th birthday of James Lepowsky and Robert Wilson, held from August 14–18, 2015, at the University of Notre Dame, Notre Dame, Indiana. Since their seminal work in the 1970s, Lepowsky and Wilson, their collaborators, their students, and those inspired by their work, have developed an amazing body of work intertwining the fields of Lie algebras, vertex algebras, number theory, theoretical physics, quantum groups, the representation theory of finite simple groups, and more. The papers presented here include recent results and descriptions of ongoing research initiatives representing the broad influence and deep connections brought about by the work of Lepowsky and Wilson and include a contribution by Yi-Zhi Huang summarizing some major open problems in these areas, in particular as they pertain to two-dimensional conformal field theory.
Perspectives In Lie Theory
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Author : Filippo Callegaro
language : en
Publisher: Springer
Release Date : 2017-12-07
Perspectives In Lie Theory written by Filippo Callegaro and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-07 with Mathematics categories.
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.
Lie Groups And Lie Algebras For Physicists
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Author : Ashok Das
language : en
Publisher: World Scientific
Release Date : 2014-09-03
Lie Groups And Lie Algebras For Physicists written by Ashok Das and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-03 with Science categories.
The book is intended for graduate students of theoretical physics (with a background in quantum mechanics) as well as researchers interested in applications of Lie group theory and Lie algebras in physics. The emphasis is on the inter-relations of representation theories of Lie groups and the corresponding Lie algebras.
Essays In The History Of Lie Groups And Algebraic Groups
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Author : Armand Borel
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
Essays In The History Of Lie Groups And Algebraic Groups written by Armand Borel 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 2001 with Mathematics categories.
Algebraic groups and Lie groups are important in most major areas of mathematics, occuring in diverse roles such as the symmetries of differential equations and as central figures in the Langlands program for number theory. In this book, Professor Borel looks at the development of the theory of Lie groups and algebraic groups, highlighting the evolution from the almost purely local theory at the start to the global theory that we know today. As the starting point of this passagefrom local to global, the author takes Lie's theory of local analytic transformation groups and Lie algebras. He then follows the globalization of the process in its two most important frameworks: (transcendental) differential geometry and algebraic geometry. Chapters II to IV are devoted to the former,Chapters V to VIII, to the latter.The essays in the first part of the book survey various proofs of the full reducibility of linear representations of $SL 2M$, the contributions H. Weyl to representation and invariant theory for Lie groups, and conclude with a chapter on E. Cartan's theory of symmetric spaces and Lie groups in the large.The second part of the book starts with Chapter V describing the development of the theory of linear algebraic groups in the 19th century. Many of the main contributions here are due to E. Study, E. Cartan, and above all, to L. Maurer. After being abandoned for nearly 50 years, the theory was revived by Chevalley and Kolchin and then further developed by many others. This is the focus of Chapter VI. The book concludes with two chapters on various aspects of the works of Chevalley on Lie groupsand algebraic groups and Kolchin on algebraic groups and the Galois theory of differential fields.The author brings a unique perspective to this study. As an important developer of some of the modern elements of both the differential geometric and the algebraic geometric sides of the theory, he has a particularly deep appreciation of the underlying mathematics. His lifelong involvement and his historical research in the subject give him a special appreciation of the story of its development.
Vertex Algebras And Algebraic Curves
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Author : Edward Frenkel
language : en
Publisher: American Mathematical Soc.
Release Date : 2004-08-25
Vertex Algebras And Algebraic Curves written by Edward Frenkel 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 2004-08-25 with Mathematics categories.
Vertex algebras are algebraic objects that encapsulate the concept of operator product expansion from two-dimensional conformal field theory. Vertex algebras are fast becoming ubiquitous in many areas of modern mathematics, with applications to representation theory, algebraic geometry, the theory of finite groups, modular functions, topology, integrable systems, and combinatorics. This book is an introduction to the theory of vertex algebras with a particular emphasis on the relationship with the geometry of algebraic curves. The notion of a vertex algebra is introduced in a coordinate-independent way, so that vertex operators become well defined on arbitrary smooth algebraic curves, possibly equipped with additional data, such as a vector bundle. Vertex algebras then appear as the algebraic objects encoding the geometric structure of various moduli spaces associated with algebraic curves. Therefore they may be used to give a geometric interpretation of various questions of representation theory. The book contains many original results, introduces important new concepts, and brings new insights into the theory of vertex algebras. The authors have made a great effort to make the book self-contained and accessible to readers of all backgrounds. Reviewers of the first edition anticipated that it would have a long-lasting influence on this exciting field of mathematics and would be very useful for graduate students and researchers interested in the subject. This second edition, substantially improved and expanded, includes several new topics, in particular an introduction to the Beilinson-Drinfeld theory of factorization algebras and the geometric Langlands correspondence.
Generalized Vertex Algebras And Relative Vertex Operators
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Author : Chongying Dong
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Generalized Vertex Algebras And Relative Vertex Operators written by Chongying Dong 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 2012-12-06 with Mathematics categories.
The rapidly-evolving theory of vertex operator algebras provides deep insight into many important algebraic structures. Vertex operator algebras can be viewed as "complex analogues" of both Lie algebras and associative algebras. The monograph is written in a n accessible and self-contained manner, with detailed proofs and with many examples interwoven through the axiomatic treatment as motivation and applications. It will be useful for research mathematicians and theoretical physicists working the such fields as representation theory and algebraic structure sand will provide the basis for a number of graduate courses and seminars on these and related topics.