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Author : Roman M. Cherniha
Publisher : MDPI
Page : 427 pages
File Size : 54,5 Mb
Release : 2018-07-06
Category : Electronic book
ISBN : 9783038425267
This book is a printed edition of the Special Issue "Lie Theory and Its Applications" that was published in Symmetry
Author : Hasan Gündoğan
Publisher : Logos Verlag Berlin GmbH
Page : 175 pages
File Size : 50,8 Mb
Release : 2011
Category : Mathematics
ISBN : 9783832530242
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.
Author : A Varchenko
Publisher : World Scientific
Page : 384 pages
File Size : 44,9 Mb
Release : 1995-03-29
Category : Mathematics
ISBN : 9789814501620
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.
Author : P.M. Cohn
Publisher : CRC Press
Page : 244 pages
File Size : 51,8 Mb
Release : 1994-07-01
Category : Mathematics
ISBN : 0412552809
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.
Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 43,6 Mb
Release : 1951
Category : Groundwater
ISBN : UCR:31210018582831
Author : Ronghua Liang,Zhigeng Pan,Adrian Cheok,Michael Haller,Rynson W.H. Lau,Hideo Saito
Publisher : Springer Science & Business Media
Page : 1367 pages
File Size : 44,8 Mb
Release : 2006-11-20
Category : Computers
ISBN : 9783540497769
This book constitutes the refereed proceedings of the 16th International Conference on Artificial Reality and Telexistence, ICAT 2006, held in Hangzhou, China in November/December 2006. The 138 revised papers cover anthropomorphic intelligent robotics, artificial life, augmented reality, distributed and collaborative VR system, motion tracking, real time computer simulation virtual reality, as well as VR interaction and navigation techniques.
Author : Doebner Heinz-dietrich,Hilgert Joachim,Dobrev Vladimir K
Publisher : World Scientific
Page : 400 pages
File Size : 47,6 Mb
Release : 1998-12-07
Category : Electronic
ISBN : 9789814544658
This book consists of about 20 lectures on theoretical and observational aspects of astrophysical black holes, by experts in the field. The basic principles and astrophysical applications of the black hole magnetosphere and the Blandford-Znajek process are reviewed in detail, as well as accretion by black holes, black hole X-Ray binaries, black holes with cosmic strings, and so on. Recent advances in X-Ray observations of galactic black holes and new understanding of supermassive black holes in AGNs and normal galaxies are also discussed.
Author : Keith Prosser
Publisher : Lulu.com
Page : 601 pages
File Size : 48,8 Mb
Release : 2016-07-07
Category : Religion
ISBN : 9781291913804
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.
Author : M. Ganesh
Publisher : I. K. International Pvt Ltd
Page : 179 pages
File Size : 40,5 Mb
Release : 2011-10-06
Category : Electronic
ISBN : 9788189866761
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
Author : Anonim
Publisher : Unknown
Page : 420 pages
File Size : 45,9 Mb
Release : 1977
Category : Navigation
ISBN : UOM:39015023454831
Author : Valerii Berestovskii,Yurii Nikonorov
Publisher : Springer Nature
Page : 482 pages
File Size : 44,8 Mb
Release : 2020-11-05
Category : Mathematics
ISBN : 9783030566586
This book is devoted to Killing vector fields and the one-parameter isometry groups of Riemannian manifolds generated by them. It also provides a detailed introduction to homogeneous geodesics, that is, geodesics that are integral curves of Killing vector fields, presenting both classical and modern results, some very recent, many of which are due to the authors. The main focus is on the class of Riemannian manifolds with homogeneous geodesics and on some of its important subclasses. To keep the exposition self-contained the book also includes useful general results not only on geodesic orbit manifolds, but also on smooth and Riemannian manifolds, Lie groups and Lie algebras, homogeneous Riemannian manifolds, and compact homogeneous Riemannian spaces. The intended audience is graduate students and researchers whose work involves differential geometry and transformation groups.
Author : Kenneth Robert Atkins
Publisher : John Wiley & Sons
Page : 838 pages
File Size : 43,6 Mb
Release : 1976
Category : Physics
ISBN : STANFORD:36105030246594
Author : Charles Colcock JONES (the Elder.)
Publisher : Unknown
Page : 128 pages
File Size : 40,7 Mb
Release : 1852
Category : Electronic
ISBN : BL:A0017437876
Author : Gregory S. Chirikjian
Publisher : Springer Science & Business Media
Page : 383 pages
File Size : 45,6 Mb
Release : 2009-09-02
Category : Mathematics
ISBN : 9780817648039
This unique two-volume set presents the subjects of stochastic processes, information theory, and Lie groups in a unified setting, thereby building bridges between fields that are rarely studied by the same people. Unlike the many excellent formal treatments available for each of these subjects individually, the emphasis in both of these volumes is on the use of stochastic, geometric, and group-theoretic concepts in the modeling of physical phenomena. Stochastic Models, Information Theory, and Lie Groups will be of interest to advanced undergraduate and graduate students, researchers, and practitioners working in applied mathematics, the physical sciences, and engineering. Extensive exercises and motivating examples make the work suitable as a textbook for use in courses that emphasize applied stochastic processes or differential geometry.
Author : Niky Kamran,Peter J. Olver
Publisher : American Mathematical Soc.
Page : 310 pages
File Size : 40,8 Mb
Release : 1994
Category : Mathematics
ISBN : 9780821851692
This volume is devoted to a range of important new ideas arising in the applications of Lie groups and Lie algebras to Schrodinger operators and associated quantum mechanical systems. In these applications, the group does not appear as a standard symmetry group, but rather as a "hidden" symmetry group whose representation theory can still be employed to analyze at least part of the spectrum of the operator. In light of the rapid developments in this subject, a Special Session was organized at the AMS meeting at Southwest Missouri State University in March 1992 in order to bring together, perhaps for the first time, mathematicians and physicists working in closely related areas. The contributions to this volume cover Lie group methods, Lie algebras and Lie algebra cohomology, representation theory, orthogonal polynomials, q-series, conformal field theory, quantum groups, scattering theory, classical invariant theory, and other topics. This volume, which contains a good balance of research and survey papers, presents at look at some of the current development in this extraordinarily rich and vibrant area.