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Potential Theory And Geometry On Lie Groups
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Book Synopsis Potential Theory and Geometry on Lie Groups by : N. Th. Varopoulos
Download or read book Potential Theory and Geometry on Lie Groups written by N. Th. Varopoulos and published by Cambridge University Press. This book was released on 2020-10-22 with total page 625 pages. Available in PDF, EPUB and Kindle. Book excerpt: Complete account of a new classification of connected Lie groups in two classes, including open problems to motivate further study.
Book Synopsis Stratified Lie Groups and Potential Theory for Their Sub-Laplacians by : Andrea Bonfiglioli
Download or read book Stratified Lie Groups and Potential Theory for Their Sub-Laplacians written by Andrea Bonfiglioli and published by Springer Science & Business Media. This book was released on 2007-08-24 with total page 812 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an extensive treatment of Potential Theory for sub-Laplacians on stratified Lie groups. It also provides a largely self-contained presentation of stratified Lie groups, and of their Lie algebra of left-invariant vector fields. The presentation is accessible to graduate students and requires no specialized knowledge in algebra or differential geometry.
Book Synopsis Differential Geometry and Lie Groups for Physicists by : Marián Fecko
Download or read book Differential Geometry and Lie Groups for Physicists written by Marián Fecko and published by Cambridge University Press. This book was released on 2006-10-12 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering subjects including manifolds, tensor fields, spinors, and differential forms, this textbook introduces geometrical topics useful in modern theoretical physics and mathematics. It develops understanding through over 1000 short exercises, and is suitable for advanced undergraduate or graduate courses in physics, mathematics and engineering.
Book Synopsis Theory of Lie Groups by : Claude Chevalley
Download or read book Theory of Lie Groups written by Claude Chevalley and published by Courier Dover Publications. This book was released on 2018-03-30 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: The standard text on the subject for many years, this introductory treatment covers classical linear groups, topological groups, manifolds, analytic groups, differential calculus of Cartan, and compact Lie groups and their representations. 1946 edition.
Book Synopsis Geometry, Lie Theory and Applications by : Sigbjørn Hervik
Download or read book Geometry, Lie Theory and Applications written by Sigbjørn Hervik and published by Springer Nature. This book was released on 2022-02-07 with total page 337 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of contributions from the participants of the Abel Symposium 2019 held in Ålesund, Norway. It was centered about applications of the ideas of symmetry and invariance, including equivalence and deformation theory of geometric structures, classification of differential invariants and invariant differential operators, integrability analysis of equations of mathematical physics, progress in parabolic geometry and mathematical aspects of general relativity. The chapters are written by leading international researchers, and consist of both survey and research articles. The book gives the reader an insight into the current research in differential geometry and Lie theory, as well as applications of these topics, in particular to general relativity and string theory.
Book Synopsis An Introduction to Lie Groups and Lie Algebras by : Alexander A. Kirillov
Download or read book An Introduction to Lie Groups and Lie Algebras written by Alexander A. Kirillov and published by Cambridge University Press. This book was released on 2008-07-31 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to semisimple Lie algebras. It is concise and informal, with numerous exercises and examples.
Book Synopsis Lectures on Lie Groups by : J. F. Adams
Download or read book Lectures on Lie Groups written by J. F. Adams and published by University of Chicago Press. This book was released on 1982 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: "[Lectures in Lie Groups] fulfills its aim admirably and should be a useful reference for any mathematician who would like to learn the basic results for compact Lie groups. . . . The book is a well written basic text [and Adams] has done a service to the mathematical community."—Irving Kaplansky
Book Synopsis Introduction To Compact Lie Groups by : Howard D Fegan
Download or read book Introduction To Compact Lie Groups written by Howard D Fegan and published by World Scientific Publishing Company. This book was released on 1991-07-30 with total page 147 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are two approaches to compact lie groups: by computation as matrices or theoretically as manifolds with a group structure. The great appeal of this book is the blending of these two approaches. The theoretical results are illustrated by computations and the theory provides a commentary on the computational work. Indeed, there are extensive computations of the structure and representation theory for the classical groups SU(n), SO(n) and Sp(n). A second exciting feature is that the differential geometry of a compact Lie group, both the classical curvature studies and the more recent heat equation methods, are treated. A large number of formulas for the connection and curvature are conveniently gathered together.This book provides an excellent text for a first course in compact Lie groups.
Book Synopsis Lectures on Lie Groups by : Wu Yi Hsiang
Download or read book Lectures on Lie Groups written by Wu Yi Hsiang and published by World Scientific. This book was released on 2000 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable book provides a concise and systematic introduction to the theory of compact connected Lie groups and their representations, as well as a complete presentation of the structure and classification theory. It uses a non-traditional approach and organization. There is a proper balance between, and a natural combination of, the algebraic and geometric aspects of Lie theory, not only in technical proofs but also in conceptual viewpoints. For example, the orbital geometry of adjoint action, is regarded as the geometric organization of the totality of non-commutativity of a given compact connected Lie group, while the maximal tori theorem of . Cartan and the Weyl reduction of the adjoint action on G to the Weyl group action on a chosen maximal torus are presented as the key results that provide a clear-cut understanding of the orbital geometry.
Book Synopsis Hardy Inequalities on Homogeneous Groups by : Michael Ruzhansky
Download or read book Hardy Inequalities on Homogeneous Groups written by Michael Ruzhansky and published by Springer. This book was released on 2019-07-02 with total page 579 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book provides an extensive treatment of Hardy inequalities and closely related topics from the point of view of Folland and Stein's homogeneous (Lie) groups. The place where Hardy inequalities and homogeneous groups meet is a beautiful area of mathematics with links to many other subjects. While describing the general theory of Hardy, Rellich, Caffarelli-Kohn-Nirenberg, Sobolev, and other inequalities in the setting of general homogeneous groups, the authors pay particular attention to the special class of stratified groups. In this environment, the theory of Hardy inequalities becomes intricately intertwined with the properties of sub-Laplacians and subelliptic partial differential equations. These topics constitute the core of this book and they are complemented by additional, closely related topics such as uncertainty principles, function spaces on homogeneous groups, the potential theory for stratified groups, and the potential theory for general Hörmander's sums of squares and their fundamental solutions. This monograph is the winner of the 2018 Ferran Sunyer i Balaguer Prize, a prestigious award for books of expository nature presenting the latest developments in an active area of research in mathematics. As can be attested as the winner of such an award, it is a vital contribution to literature of analysis not only because it presents a detailed account of the recent developments in the field, but also because the book is accessible to anyone with a basic level of understanding of analysis. Undergraduate and graduate students as well as researchers from any field of mathematical and physical sciences related to analysis involving functional inequalities or analysis of homogeneous groups will find the text beneficial to deepen their understanding.
Book Synopsis Lie Groups, Physics, and Geometry by : Robert Gilmore
Download or read book Lie Groups, Physics, and Geometry written by Robert Gilmore and published by Cambridge University Press. This book was released on 2008-01-17 with total page 5 pages. Available in PDF, EPUB and Kindle. Book excerpt: Describing many of the most important aspects of Lie group theory, this book presents the subject in a 'hands on' way. Rather than concentrating on theorems and proofs, the book shows the applications of the material to physical sciences and applied mathematics. Many examples of Lie groups and Lie algebras are given throughout the text. The relation between Lie group theory and algorithms for solving ordinary differential equations is presented and shown to be analogous to the relation between Galois groups and algorithms for solving polynomial equations. Other chapters are devoted to differential geometry, relativity, electrodynamics, and the hydrogen atom. Problems are given at the end of each chapter so readers can monitor their understanding of the materials. This is a fascinating introduction to Lie groups for graduate and undergraduate students in physics, mathematics and electrical engineering, as well as researchers in these fields.
Book Synopsis Lie Groups, Lie Algebras, and Their Representations by : V.S. Varadarajan
Download or read book Lie Groups, Lie Algebras, and Their Representations written by V.S. Varadarajan and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book has grown out of a set of lecture notes I had prepared for a course on Lie groups in 1966. When I lectured again on the subject in 1972, I revised the notes substantially. It is the revised version that is now appearing in book form. The theory of Lie groups plays a fundamental role in many areas of mathematics. There are a number of books on the subject currently available -most notably those of Chevalley, Jacobson, and Bourbaki-which present various aspects of the theory in great depth. However, 1 feei there is a need for a single book in English which develops both the algebraic and analytic aspects of the theory and which goes into the representation theory of semi simple Lie groups and Lie algebras in detail. This book is an attempt to fiii this need. It is my hope that this book will introduce the aspiring graduate student as well as the nonspecialist mathematician to the fundamental themes of the subject. I have made no attempt to discuss infinite-dimensional representations. This is a very active field, and a proper treatment of it would require another volume (if not more) of this size. However, the reader who wants to take up this theory will find that this book prepares him reasonably well for that task.
Book Synopsis Geometric Potential Analysis by : Mario Milman
Download or read book Geometric Potential Analysis written by Mario Milman and published by Walter de Gruyter GmbH & Co KG. This book was released on 2022-06-21 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph contains papers that were delivered at the special session on Geometric Potential Analysis, that was part of the Mathematical Congress of the Americas 2021, virtually held in Buenos Aires. The papers, that were contributed by renowned specialists worldwide, cover important aspects of current research in geometrical potential analysis and its applications to partial differential equations and mathematical physics.
Book Synopsis Potential Theory on Stratified Lie Groups by : Mishra Mukund Madhav
Download or read book Potential Theory on Stratified Lie Groups written by Mishra Mukund Madhav and published by Independent Author. This book was released on 2022-11-07 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: The potential theory is a broad area of study of properties of functions that satisfy the Laplace equation. The major topics covered under potential theory are harmonic and subharmonic functions, Green's function, Dirichlet boundary value problem, capacity, polar sets, thin sets, and generalized Dirichlet problem. On stratified Lie groups, we have an analog of the Euclidean Laplacian which happens to be a hypoelliptictic operator and therefore it is interesting to study potential theory on stratified Lie groups. In this thesis, we have studied some problems involving the sub-Laplacian and their powers on certain two-step nilpotent stratified Lie groups. The thesis is divided into five chapters followed by a bibliography, list of notations, and index. The first chapter is an introduction. In this chapter, we have introduced some basic notions of the theory of partial differential equations, distributions, the potential theory of stratified Lie groups, and the Heisenberg group. We have stated the results required in the thesis without proof and proper references are given for details of the topics and theorems discussed.
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.
Download or read book Lie Groups I written by Mikio Ise and published by American Mathematical Soc.. This book was released on 1991 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a wide range of problems connected with rational approximations of numbers and analytic functions; these problems touch on many topics in contemporary analysis, such as analytic functions, orthogonal polynomials, spectral theory of operators, and potential theory.
Download or read book Matrix Groups written by Andrew Baker and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a first taste of the theory of Lie groups, focusing mainly on matrix groups: closed subgroups of real and complex general linear groups. The first part studies examples and describes classical families of simply connected compact groups. The second section introduces the idea of a lie group and explores the associated notion of a homogeneous space using orbits of smooth actions. The emphasis throughout is on accessibility.
