Lie Algebras Theory And Algorithms

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Lie Algebras Theory And Algorithms

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Author : W.A. de Graaf
language : en
Publisher: Elsevier
Release Date : 2000-02-04

Lie Algebras Theory And Algorithms written by W.A. de Graaf and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-02-04 with Mathematics categories.

The aim of the present work is two-fold. Firstly it aims at a giving an account of many existing algorithms for calculating with finite-dimensional Lie algebras. Secondly, the book provides an introduction into the theory of finite-dimensional Lie algebras. These two subject areas are intimately related. First of all, the algorithmic perspective often invites a different approach to the theoretical material than the one taken in various other monographs (e.g., [42], [48], [77], [86]). Indeed, on various occasions the knowledge of certain algorithms allows us to obtain a straightforward proof of theoretical results (we mention the proof of the Poincaré-Birkhoff-Witt theorem and the proof of Iwasawa's theorem as examples). Also proofs that contain algorithmic constructions are explicitly formulated as algorithms (an example is the isomorphism theorem for semisimple Lie algebras that constructs an isomorphism in case it exists). Secondly, the algorithms can be used to arrive at a better understanding of the theory. Performing the algorithms in concrete examples, calculating with the concepts involved, really brings the theory of life.

Lie Algebras

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Author : Willem A. De Graaf
language : en
Publisher:
Release Date : 2000

Lie Algebras written by Willem A. De Graaf and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Lie algebras categories.

The aim of the present work is two-fold. Firstly it aims at a giving an account of many existing algorithms for calculating with finite-dimensional Lie algebras. Secondly, the book provides an introduction into the theory of finite-dimensional Lie algebras. These two subject areas are intimately related. First of all, the algorithmic perspective often invites a different approach to the theoretical material than the one taken in various other monographs (e.g., [42], [48], [77], [86]). Indeed, on various occasions the knowledge of certain algorithms allows us to obtain a straightforward proof of theoretical results (we mention the proof of the Poincaré-Birkhoff-Witt theorem and the proof of Iwasawa's theorem as examples). Also proofs that contain algorithmic constructions are explicitly formulated as algorithms (an example is the isomorphism theorem for semisimple Lie algebras that constructs an isomorphism in case it exists). Secondly, the algorithms can be used to arrive at a better understanding of the theory. Performing the algorithms in concrete examples, calculating with the concepts involved, really brings the theory of life.

Lie Group Machine Learning

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Author : Fanzhang Li
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-11-05

Lie Group Machine Learning written by Fanzhang Li and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-05 with Computers categories.

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.

Basic Lie Theory

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Author : Hossein Abbaspour
language : en
Publisher: World Scientific
Release Date : 2007

Basic Lie Theory written by Hossein Abbaspour and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Science categories.

This volume provides a comprehensive treatment of basic Lie theory, primarily directed toward graduate study. The text is ideal for a full graduate course in Lie groups and Lie algebras. However, the book is also very usable for a variety of other courses: a one-semester course in Lie algebras, or on Haar measure and its applications, for advanced undergraduates; or as the text for one-semester graduate courses in Lie groups and symmetric spaces of non-compact type, or in lattices in Lie groups. The material is complete and detailed enough to be used for self-study; it can also serve as a reference work for professional mathematicians working in other areas. The book's utility for such a varied readership is enhanced by a diagram showing the interdependence of the separate chapters so that individual chapters and the material they depend upon can be selected, while others can be skipped.The book incorporates many of the most significant discoveries and pioneering contributions of the masters of the subject: Borel, Cartan, Chevalley, Iwasawa, Mostow, Siegel, and Weyl, among others.

Computer Algebra And Polynomials

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Author : Jaime Gutierrez
language : en
Publisher: Springer
Release Date : 2015-01-20

Computer Algebra And Polynomials written by Jaime Gutierrez and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-20 with Computers categories.

Algebra and number theory have always been counted among the most beautiful mathematical areas with deep proofs and elegant results. However, for a long time they were not considered that important in view of the lack of real-life applications. This has dramatically changed: nowadays we find applications of algebra and number theory frequently in our daily life. This book focuses on the theory and algorithms for polynomials over various coefficient domains such as a finite field or ring. The operations on polynomials in the focus are factorization, composition and decomposition, basis computation for modules, etc. Algorithms for such operations on polynomials have always been a central interest in computer algebra, as it combines formal (the variables) and algebraic or numeric (the coefficients) aspects. The papers presented were selected from the Workshop on Computer Algebra and Polynomials, which was held in Linz at the Johann Radon Institute for Computational and Applied Mathematics (RICAM) during November 25-29, 2013, at the occasion of the Special Semester on Applications of Algebra and Number Theory.

Computation With Linear Algebraic Groups

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Author : Willem Adriaan de Graaf
language : en
Publisher: CRC Press
Release Date : 2017-08-07

Computation With Linear Algebraic Groups written by Willem Adriaan de Graaf and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-07 with Mathematics categories.

Designed as a self-contained account of a number of key algorithmic problems and their solutions for linear algebraic groups, this book combines in one single text both an introduction to the basic theory of linear algebraic groups and a substantial collection of useful algorithms. Computation with Linear Algebraic Groups offers an invaluable guide to graduate students and researchers working in algebraic groups, computational algebraic geometry, and computational group theory, as well as those looking for a concise introduction to the theory of linear algebraic groups.

Computer Aided Systems Theory Eurocast 2009

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Author : Roberto Moreno-Díaz
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-10-08

Computer Aided Systems Theory Eurocast 2009 written by Roberto Moreno-Díaz 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 2009-10-08 with Computers categories.

This book constitutes the thoroughly refereed post-proceedings of the 12th International Conference on Computer Aided Systems Theory, EUROCAST 2009, held in Las Palmas de Gran Canaria, Spain in February 2009. The 120 revised full papers presented were carefully reviewed and selected for inclusion in the book. The papers are organized in topical sections on systems theory and simulation: formal approaches, computation and simulation in modeling biological Systems, intelligent information processing, applied formal verification, computer vision and image processing, mobile and autonomous systems: robots and cars, simulation based system optimization, signal processing methods in systems design and cybernetics, polynomial models in control system design, heurist problem solving, simulation and formal methods in systems design and engineering, models of co-operative engineering systems.

Mathematical Software Icms 2014

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Author : Hoon Hong
language : en
Publisher: Springer
Release Date : 2014-08-01

Mathematical Software Icms 2014 written by Hoon Hong and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-01 with Computers categories.

This book constitutes the proceedings of the 4th International Conference on Mathematical Software, ICMS 2014, held in Seoul, South Korea, in August 2014. The 108 papers included in this volume were carefully reviewed and selected from 150 submissions. The papers are organized in topical sections named: invited; exploration; group; coding; topology; algebraic; geometry; surfaces; reasoning; special; Groebner; triangular; parametric; interfaces and general.

The Diverse World Of Pdes

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Author : I. S. Krasil′shchik
language : en
Publisher: American Mathematical Society
Release Date : 2023-08-23

The Diverse World Of Pdes written by I. S. Krasil′shchik and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-23 with Mathematics categories.

This volume contains the proceedings of the Alexandre Vinogradov Memorial Conference on Diffieties, Cohomological Physics, and Other Animals, held from December 13–17, 2021, at Independent University of Moscow and Moscow State University, Moscow, Russia. The papers reflect the modern interplay between partial differential equations and various aspects of algebra and computer science. The topics discussed are: relations between integrability and differential rings, supermanifolds, differential calculus over graded algebras, noncommutative generalizations of PDEs, quantum vector fields, generalized Nijenhuis torsion, cohomological approach to the geometry of differential equations, the argument shift method, Frölicher structures in the formal Kadomtsev–Petviashvili hierarchy, and computer-based determination of optimal systems of Lie subalgebras. The companion volume (Contemporary Mathematics, Volume 788) is devoted to Geometry and Mathematical Physics.

Basics Of Representation Theory

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Author : Udayan Bhattacharya
language : en
Publisher: Educohack Press
Release Date : 2025-02-20

Basics Of Representation Theory written by Udayan Bhattacharya and has been published by Educohack Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-02-20 with Science categories.

Delve into the captivating world of "Basics of Representation Theory," a comprehensive guide designed for students, researchers, and enthusiasts eager to explore the intricate symmetries and structures that underpin modern mathematics. Our book offers a detailed introduction to foundational concepts, providing a solid understanding of group actions, linear representations, and character theory. From there, it explores the algebraic structures of irreducible representations, breaking down the decomposition into irreducible components and examining the properties of characters. Readers will journey through diverse topics, including the representation theory of symmetric groups, Lie groups, and algebraic groups, as well as advanced topics such as the representation theory of finite groups, the Langlands program, and applications in quantum mechanics and number theory. With a wealth of examples, illustrations, and exercises, "Basics of Representation Theory" ensures a hands-on approach to learning, encouraging practical exploration and problem-solving. The book also includes numerous references and further reading suggestions for those who wish to delve deeper into specific topics. Written in a clear and accessible style, this book caters to all levels, from undergraduate students encountering representation theory for the first time to experienced researchers seeking fresh insights. With its comprehensive coverage and diverse applications, "Basics of Representation Theory" is an invaluable resource for anyone interested in the beauty and depth of this field.