Lie and non Lie Symmetries Theory and Applications for Solving Nonlinear Models

Lie and non Lie Symmetries  Theory and Applications for Solving Nonlinear Models
Author: Roman M. Cherniha
Publsiher: MDPI
Total Pages: 427
Release: 2018-07-06
Genre: Electronic book
ISBN: 9783038425267

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This book is a printed edition of the Special Issue "Lie Theory and Its Applications" that was published in Symmetry

Classification and Structure Theory of Lie Algebras of Smooth Sections

Classification and Structure Theory of Lie Algebras of Smooth Sections
Author: Hasan Gündoğan
Publsiher: Logos Verlag Berlin GmbH
Total Pages: 175
Release: 2011
Genre: Mathematics
ISBN: 9783832530242

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Lie groups and their "derived objects", Lie algebras, appear in various fields of mathematics and physics. At least since the beginning of the 20th century, and after the famous works of Wilhelm Killing, Elie Cartan, Eugenio Elia Levi, Anatoly Malcev and Igor Ado on the structure of finite-dimensional Lie algebras, the classification and structure theory of infinite-dimensional Lie algebras has become an interesting and fairly vast field of interest. This dissertation focusses on the structure of Lie algebras of smooth and k-times differentiable sections of finite-dimensional Lie algebra bundles, which are generalizations of the famous and well-understood affine Kac-Moody algebras. Besides answering the immediate structural questions (center, commutator algebra, derivations, centroid, automorphism group), this work approaches a classification of section algebras by homotopy theory. Furthermore, we determine a universal invariant symmetric bilinear form on Lie algebras of smooth sections and use this form to define a natural central extension which is universal, at least in the case of Lie algebra bundles with compact base manifold.

Elements of Linear Algebra

Elements of Linear Algebra
Author: P.M. Cohn
Publsiher: Routledge
Total Pages: 241
Release: 2017-10-19
Genre: Mathematics
ISBN: 9781351452847

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This volume presents a thorough discussion of systems of linear equations and their solutions. Vectors and matrices are introduced as required and an account of determinants is given. Great emphasis has been placed on keeping the presentation as simple as possible, with many illustrative examples. While all mathematical assertions are proved, the student is led to view the mathematical content intuitively, as an aid to understanding.The text treats the coordinate geometry of lines, planes and quadrics, provides a natural application for linear algebra and at the same time furnished a geometrical interpretation to illustrate the algebraic concepts.

Nilpotent Lie Algebras

Nilpotent Lie Algebras
Author: M. Goze,Y. Khakimdjanov
Publsiher: Springer Science & Business Media
Total Pages: 350
Release: 2013-11-27
Genre: Mathematics
ISBN: 9789401724326

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This volume is devoted to the theory of nilpotent Lie algebras and their applications. Nilpotent Lie algebras have played an important role over the last years both in the domain of algebra, considering its role in the classification problems of Lie algebras, and in the domain of differential geometry. Among the topics discussed here are the following: cohomology theory of Lie algebras, deformations and contractions, the algebraic variety of the laws of Lie algebras, the variety of nilpotent laws, and characteristically nilpotent Lie algebras in nilmanifolds. Audience: This book is intended for graduate students specialising in algebra, differential geometry and in theoretical physics and for researchers in mathematics and in theoretical physics.

Basics of Computer Aided Geometric Design

Basics of Computer Aided Geometric Design
Author: M. Ganesh
Publsiher: I. K. International Pvt Ltd
Total Pages: 179
Release: 2011-10-06
Genre: Electronic Book
ISBN: 9788189866761

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The aim of the book is to provide a good foundation of Computer-Aided Geometric Design to students who are doing under-graduate courses in engineering, especially Mechanical Engineering, Computer Science, Geometric Modeling and CAD/CAM. This book is organized in two parts. Part-I deals with the basics of differential geometry of curves and surface, a good understanding of which is essential prerequisite to what follows in the Part-II. Part-II is devoted entirely to the geometric designs of curves and surfaces, which are used in the development of computer graphics and profiles and hulls of ships, aircraft wings, satellites (to name a few large scale products) as also telephones, mobile phones, fancy flower vases (to name a few small-scale products). Concepts introduced are illustrated with examples, which are completely worked out. A list of problems is also given at the end of each chapter

Preface Miracles The Synoptic gospels pt 1 v 2 The Synoptic gospels pt 2 The Fourth gospel v 3 The Acts of the apostles The direct evidence for miracles The resurrection and ascension

Preface  Miracles  The Synoptic gospels  pt  1   v  2  The Synoptic gospels  pt  2  The Fourth gospel   v  3  The Acts of the apostles  The direct evidence for miracles  The resurrection and ascension
Author: Walter Richard Cassels
Publsiher: Unknown
Total Pages: 600
Release: 1879
Genre: Bible
ISBN: UCAL:$B109355

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Multidimensional Hypergeometric Functions and Representation Theory of Lie Algebras and Quantum Groups

Multidimensional Hypergeometric Functions and Representation Theory of Lie Algebras and Quantum Groups
Author: A Varchenko
Publsiher: World Scientific
Total Pages: 384
Release: 1995-03-29
Genre: Mathematics
ISBN: 9789814501620

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This book recounts the connections between multidimensional hypergeometric functions and representation theory. In 1984, physicists Knizhnik and Zamolodchikov discovered a fundamental differential equation describing correlation functions in conformal field theory. The equation is defined in terms of a Lie algebra. Kohno and Drinfeld found that the monodromy of the differential equation is described in terms of the quantum group associated with the Lie algebra. It turns out that this phenomenon is the tip of the iceberg. The Knizhnik–Zamolodchikov differential equation is solved in multidimensional hypergeometric functions, and the hypergeometric functions yield the connection between the representation theories of Lie algebras and quantum groups. The topics presented in this book are not adequately covered in periodicals. Contents:IntroductionConstruction of Complexes Calculating Homology of the Complement of a ConfigurationConstruction of Homology Complexes for Discriminantal ConfigurationAlgebraic Interpretation of Chain Complexes of a Discriminantal ConfigurationQuasiisomorphism of Two-Sided Hochschild Complexes to Suitable One-Sided Hochschild ComplexesBundle Properties of a Discriminantal ConfigurationR-Matrix for the Two-Sided Hochschild ComplexesMonodromyR-Matrix Operator as the Canonical Element, Quantum DoublesHypergeometric IntegralsKac–Moody Lie Algebras Without Serre's Relations and Their DoublesHypergeometric Integrals of a Discriminantal ConfigurationResonances at InfinityDegenerations of Discriminantal ConfigurationsRemarks on Homology Groups of a Configuration with Coefficients in Local Systems More General than Complex One-Dimensional Readership: Mathematicians, theoretical physicists, and graduate students. keywords:Hypergeometric Function;Hypergeometric Type Function;Hypergeometric Integral;Kac-Moody Algebra;Quantum Group;Representations of a Kac-Moody Algebra;Representations of a Quantum Group;Discriminant Configuration;Monodromy “The book is elegantly structured and sticks closely to the point, and is also fairly down to earth … as well as serving as an excellent specialist monograph, it should also be useful as a first exposure to these topics for anyone who likes to learn a subject through the study of a concrete problem.” Bull. London Math. Soc.

Was Jesus Crucified

Was Jesus Crucified
Author: Keith Prosser
Publsiher: Lulu.com
Total Pages: 601
Release: 2016-07-07
Genre: Religion
ISBN: 9781291913804

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An historical research into the life and death of Jesus Christ as described in the Christian Holy Bible. Examines early Gnostic, Jewish, Roman, Greek, Syrian and Christian historical sources, to give a near-comprehensive analysis of the subject, resulting in a genuine fresh look into the well studied topic. A meticulous review is made of what Josephus wrote about Jesus through critical analysis demonstrating why he must have written it. A similar examination is made of the Gnostic writings especially the Nag Hammadi gospel of Thomas, resulting in textual proof he wrote it after the Bible's gospels. The book should prove of great interest to those studying or reading the New Testament as it includes a summarised history of the Faith spanning from the present day to the first century, the origins of present day scepticism, introduction into manuscript preservation, and a glossary of theological terms and early Christian controversies.