Modern Trends In Lie Algebra Representation Theory

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Modern Trends in Algebra and Representation Theory

Author : David Jordan
Publisher : Cambridge University Press
ISBN 13 : 1009103474
Total Pages : 408 pages
Book Rating : 4.0/5 (91 download)

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Book Synopsis Modern Trends in Algebra and Representation Theory by : David Jordan

Download or read book Modern Trends in Algebra and Representation Theory written by David Jordan and published by Cambridge University Press. This book was released on 2023-07-31 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: Expanding upon the material delivered during the LMS Autumn Algebra School 2020, this volume reflects the fruitful connections between different aspects of representation theory. Each survey article addresses a specific subject from a modern angle, beginning with an exploration of the representation theory of associative algebras, followed by the coverage of important developments in Lie theory in the past two decades, before the final sections introduce the reader to three strikingly different aspects of group theory. Written at a level suitable for graduate students and researchers in related fields, this book provides pure mathematicians with a springboard into the vast and growing literature in each area.

Modern Trends in Lie Algebra Representation Theory

Author : Albert John Coleman
Publisher : Kingston, Ont. : Queen's University
ISBN 13 :
Total Pages : 118 pages
Book Rating : 4.3/5 (243 download)

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Book Synopsis Modern Trends in Lie Algebra Representation Theory by : Albert John Coleman

Download or read book Modern Trends in Lie Algebra Representation Theory written by Albert John Coleman and published by Kingston, Ont. : Queen's University. This book was released on 1994 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lie Theory and Its Applications in Physics

Author : Vladimir Dobrev
Publisher : Springer Nature
ISBN 13 : 9811577757
Total Pages : 552 pages
Book Rating : 4.8/5 (115 download)

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Book Synopsis Lie Theory and Its Applications in Physics by : Vladimir Dobrev

Download or read book Lie Theory and Its Applications in Physics written by Vladimir Dobrev and published by Springer Nature. This book was released on 2020-10-15 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents modern trends in the area of symmetries and their applications based on contributions to the workshop "Lie Theory and Its Applications in Physics" held near Varna (Bulgaria) in June 2019. Traditionally, Lie theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry, which is very helpful in understanding its structure. Geometrization and symmetries are meant in their widest sense, i.e., representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators, special functions, and others. Furthermore, the necessary tools from functional analysis are included. This is a large interdisciplinary and interrelated field. The topics covered in this volume from the workshop represent the most modern trends in the field : Representation Theory, Symmetries in String Theories, Symmetries in Gravity Theories, Supergravity, Conformal Field Theory, Integrable Systems, Polylogarithms, and Supersymmetry. They also include Supersymmetric Calogero-type models, Quantum Groups, Deformations, Quantum Computing and Deep Learning, Entanglement, Applications to Quantum Theory, and Exceptional Quantum Algebra for the standard model of particle physics This book is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists, including researchers and graduate students interested in Lie Theory.

Representation Theory of Finite Monoids

Author : Benjamin Steinberg
Publisher : Springer
ISBN 13 : 3319439324
Total Pages : 324 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Representation Theory of Finite Monoids by : Benjamin Steinberg

Download or read book Representation Theory of Finite Monoids written by Benjamin Steinberg and published by Springer. This book was released on 2016-12-09 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first text on the subject provides a comprehensive introduction to the representation theory of finite monoids. Carefully worked examples and exercises provide the bells and whistles for graduate accessibility, bringing a broad range of advanced readers to the forefront of research in the area. Highlights of the text include applications to probability theory, symbolic dynamics, and automata theory. Comfort with module theory, a familiarity with ordinary group representation theory, and the basics of Wedderburn theory, are prerequisites for advanced graduate level study. Researchers in algebra, algebraic combinatorics, automata theory, and probability theory, will find this text enriching with its thorough presentation of applications of the theory to these fields. Prior knowledge of semigroup theory is not expected for the diverse readership that may benefit from this exposition. The approach taken in this book is highly module-theoretic and follows the modern flavor of the theory of finite dimensional algebras. The content is divided into 7 parts. Part I consists of 3 preliminary chapters with no prior knowledge beyond group theory assumed. Part II forms the core of the material giving a modern module-theoretic treatment of the Clifford –Munn–Ponizovskii theory of irreducible representations. Part III concerns character theory and the character table of a monoid. Part IV is devoted to the representation theory of inverse monoids and categories and Part V presents the theory of the Rhodes radical with applications to triangularizability. Part VI features 3 chapters devoted to applications to diverse areas of mathematics and forms a high point of the text. The last part, Part VII, is concerned with advanced topics. There are also 3 appendices reviewing finite dimensional algebras, group representation theory, and Möbius inversion.

Lie Group Machine Learning

Author : Fanzhang Li
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110499509
Total Pages : 534 pages
Book Rating : 4.1/5 (14 download)

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Book Synopsis Lie Group Machine Learning by : Fanzhang Li

Download or read book Lie Group Machine Learning written by Fanzhang Li and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-11-05 with total page 534 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explains deep learning concepts and derives semi-supervised learning and nuclear learning frameworks based on cognition mechanism and Lie group theory. Lie group machine learning is a theoretical basis for brain intelligence, Neuromorphic learning (NL), advanced machine learning, and advanced artifi cial intelligence. The book further discusses algorithms and applications in tensor learning, spectrum estimation learning, Finsler geometry learning, Homology boundary learning, and prototype theory. With abundant case studies, this book can be used as a reference book for senior college students and graduate students as well as college teachers and scientific and technical personnel involved in computer science, artifi cial intelligence, machine learning, automation, mathematics, management science, cognitive science, financial management, and data analysis. In addition, this text can be used as the basis for teaching the principles of machine learning. Li Fanzhang is professor at the Soochow University, China. He is director of network security engineering laboratory in Jiangsu Province and is also the director of the Soochow Institute of industrial large data. He published more than 200 papers, 7 academic monographs, and 4 textbooks. Zhang Li is professor at the School of Computer Science and Technology of the Soochow University. She published more than 100 papers in journals and conferences, and holds 23 patents. Zhang Zhao is currently an associate professor at the School of Computer Science and Technology of the Soochow University. He has authored and co-authored more than 60 technical papers.

New Trends in Algebras and Combinatorics

Author : K. P. Shum
Publisher :
ISBN 13 : 9811215472
Total Pages : 498 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis New Trends in Algebras and Combinatorics by : K. P. Shum

Download or read book New Trends in Algebras and Combinatorics written by K. P. Shum and published by . This book was released on 2020 with total page 498 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Geometric Representation Theory and Extended Affine Lie Algebras

Author : Erhard Neher
Publisher : American Mathematical Soc.
ISBN 13 : 082185237X
Total Pages : 226 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Geometric Representation Theory and Extended Affine Lie Algebras by : Erhard Neher

Download or read book Geometric Representation Theory and Extended Affine Lie Algebras written by Erhard Neher and published by American Mathematical Soc.. This book was released on 2011 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Modern Trends in Hypercomplex Analysis

Author : Swanhild Bernstein
Publisher : Birkhäuser
ISBN 13 : 3319425293
Total Pages : 310 pages
Book Rating : 4.3/5 (194 download)

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Book Synopsis Modern Trends in Hypercomplex Analysis by : Swanhild Bernstein

Download or read book Modern Trends in Hypercomplex Analysis written by Swanhild Bernstein and published by Birkhäuser. This book was released on 2016-11-21 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains a selection of papers presented at the session "Quaternionic and Clifford Analysis" at the 10th ISAAC Congress held in Macau in August 2015. The covered topics represent the state-of-the-art as well as new trends in hypercomplex analysis and its applications.

Recent Developments in Quantum Affine Algebras and Related Topics

Author : Naihuan Jing
Publisher : American Mathematical Soc.
ISBN 13 : 0821811991
Total Pages : 482 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Recent Developments in Quantum Affine Algebras and Related Topics by : Naihuan Jing

Download or read book Recent Developments in Quantum Affine Algebras and Related Topics written by Naihuan Jing and published by American Mathematical Soc.. This book was released on 1999 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume reflects the proceedings of the International Conference on Representations of Affine and Quantum Affine Algebras and Their Applications held at North Carolina State University (Raleigh). In recent years, the theory of affine and quantum affine Lie algebras has become an important area of mathematical research with numerous applications in other areas of mathematics and physics. Three areas of recent progress are the focus of this volume: affine and quantum affine algebras and their generalizations, vertex operator algebras and their representations, and applications in combinatorics and statistical mechanics. Talks given by leading international experts at the conference offered both overviews on the subjects and current research results. The book nicely presents the interplay of these topics recently occupying "centre stage" in the theory of infinite dimensional Lie theory.

Trends in Representation Theory of Algebras and Related Topics

Author : Andrzej Skowroński
Publisher : European Mathematical Society
ISBN 13 : 9783037190623
Total Pages : 732 pages
Book Rating : 4.1/5 (96 download)

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Book Synopsis Trends in Representation Theory of Algebras and Related Topics by : Andrzej Skowroński

Download or read book Trends in Representation Theory of Algebras and Related Topics written by Andrzej Skowroński and published by European Mathematical Society. This book was released on 2008 with total page 732 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Lie Algebras, Vertex Operator Algebras and Their Applications

Author : Yi-Zhi Huang
Publisher : American Mathematical Soc.
ISBN 13 : 0821839861
Total Pages : 500 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Lie Algebras, Vertex Operator Algebras and Their Applications by : Yi-Zhi Huang

Download or read book Lie Algebras, Vertex Operator Algebras and Their Applications written by Yi-Zhi Huang and published by American Mathematical Soc.. This book was released on 2007 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Representations of Lie Algebras, Quantum Groups and Related Topics

Author : Naihuan Jing
Publisher : American Mathematical Soc.
ISBN 13 : 1470436965
Total Pages : 242 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Representations of Lie Algebras, Quantum Groups and Related Topics by : Naihuan Jing

Download or read book Representations of Lie Algebras, Quantum Groups and Related Topics written by Naihuan Jing and published by American Mathematical Soc.. This book was released on 2018-08-21 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the AMS Special Session on Representations of Lie Algebras, Quantum Groups and Related Topics, held from November 12–13, 2016, at North Carolina State University, Raleigh, North Carolina. The articles cover various aspects of representations of Kac–Moody Lie algebras and their applications, structure of Leibniz algebras and Krichever–Novikov algebras, representations of quantum groups, and related topics.

A Guide To Lie Systems With Compatible Geometric Structures

Author : Javier De Lucas Araujo
Publisher : World Scientific
ISBN 13 : 1786346990
Total Pages : 425 pages
Book Rating : 4.7/5 (863 download)

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Book Synopsis A Guide To Lie Systems With Compatible Geometric Structures by : Javier De Lucas Araujo

Download or read book A Guide To Lie Systems With Compatible Geometric Structures written by Javier De Lucas Araujo and published by World Scientific. This book was released on 2020-01-22 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents a comprehensive guide to the study of Lie systems from the fundamentals of differential geometry to the development of contemporary research topics. It embraces several basic topics on differential geometry and the study of geometric structures while developing known applications in the theory of Lie systems. The book also includes a brief exploration of the applications of Lie systems to superequations, discrete systems, and partial differential equations.Offering a complete overview from the topic's foundations to the present, this book is an ideal resource for Physics and Mathematics students, doctoral students and researchers.

Trends in the Representation Theory of Finite Dimensional Algebras

Author : Edward L. Green
Publisher : American Mathematical Soc.
ISBN 13 : 0821809288
Total Pages : 378 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Trends in the Representation Theory of Finite Dimensional Algebras by : Edward L. Green

Download or read book Trends in the Representation Theory of Finite Dimensional Algebras written by Edward L. Green and published by American Mathematical Soc.. This book was released on 1998 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: This refereed collection of research papers and survey articles reflects the interplay of finite-dimensional algebras with other areas (algebraic geometry, homological algebra, and the theory of quantum groups). Current trends are presented from the discussions at the AMS-IMS-SIAM Joint Summer Research Conference at the University of Washington (Seattle). The volume features several excellent expository articles which will introduce inspiration to researchers in related areas, as it includes original papers spanning a broad spectrum of representation theory.

Journal of Lie Theory

Author :
Publisher :
ISBN 13 :
Total Pages : 644 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Journal of Lie Theory by :

Download or read book Journal of Lie Theory written by and published by . This book was released on 2004 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Lie Theory and Its Applications in Physics

Author : Vladimir Dobrev
Publisher : Springer
ISBN 13 : 4431552855
Total Pages : 554 pages
Book Rating : 4.4/5 (315 download)

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Book Synopsis Lie Theory and Its Applications in Physics by : Vladimir Dobrev

Download or read book Lie Theory and Its Applications in Physics written by Vladimir Dobrev and published by Springer. This book was released on 2015-01-26 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt: Traditionally, Lie theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry which is very helpful in understanding its structure. Geometrization and symmetries are meant in their widest sense, i.e., representation theory, algebraic geometry, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear PDE, special functions, and others. Furthermore, the necessary tools from functional analysis and number theory are included. This is a big interdisciplinary and interrelated field. Samples of these fresh trends are presented in this volume, based on contributions from the Workshop "Lie Theory and Its Applications in Physics" held near Varna (Bulgaria) in June 2013. This book is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists and researchers in the field of Lie Theory.

Representations of Algebraic Groups, Quantum Groups, and Lie Algebras

Author : Georgia Benkart
Publisher : American Mathematical Soc.
ISBN 13 : 0821839241
Total Pages : 270 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Representations of Algebraic Groups, Quantum Groups, and Lie Algebras by : Georgia Benkart

Download or read book Representations of Algebraic Groups, Quantum Groups, and Lie Algebras written by Georgia Benkart 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.