Share

Geometry, Lie Theory and Applications

2022-02-07 Mathematics
Download Geometry, Lie Theory and Applications PDF Online Free

Author :
Release : 2022-02-07
Genre : Mathematics
Kind : eBook
Book Rating : 960/5 ( reviews)

GET EBOOK


Book Synopsis Geometry, Lie Theory and Applications by : Sigbjørn Hervik

Download or read book Geometry, Lie Theory and Applications written by Sigbjørn Hervik. This book was released on 2022-02-07. 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.

Lie Groups and Algebras with Applications to Physics, Geometry, and Mechanics

2013-11-11 Mathematics
Download Lie Groups and Algebras with Applications to Physics, Geometry, and Mechanics PDF Online Free

Author :
Release : 2013-11-11
Genre : Mathematics
Kind : eBook
Book Rating : 108/5 ( reviews)

GET EBOOK


Book Synopsis Lie Groups and Algebras with Applications to Physics, Geometry, and Mechanics by : D.H. Sattinger

Download or read book Lie Groups and Algebras with Applications to Physics, Geometry, and Mechanics written by D.H. Sattinger. This book was released on 2013-11-11. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended as an introductory text on the subject of Lie groups and algebras and their role in various fields of mathematics and physics. It is written by and for researchers who are primarily analysts or physicists, not algebraists or geometers. Not that we have eschewed the algebraic and geo metric developments. But we wanted to present them in a concrete way and to show how the subject interacted with physics, geometry, and mechanics. These interactions are, of course, manifold; we have discussed many of them here-in particular, Riemannian geometry, elementary particle physics, sym metries of differential equations, completely integrable Hamiltonian systems, and spontaneous symmetry breaking. Much ofthe material we have treated is standard and widely available; but we have tried to steer a course between the descriptive approach such as found in Gilmore and Wybourne, and the abstract mathematical approach of Helgason or Jacobson. Gilmore and Wybourne address themselves to the physics community whereas Helgason and Jacobson address themselves to the mathematical community. This book is an attempt to synthesize the two points of view and address both audiences simultaneously. We wanted to present the subject in a way which is at once intuitive, geometric, applications oriented, mathematically rigorous, and accessible to students and researchers without an extensive background in physics, algebra, or geometry.

Applications of Lie Groups to Differential Equations

2012-12-06 Mathematics
Download Applications of Lie Groups to Differential Equations PDF Online Free

Author :
Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 749/5 ( reviews)

GET EBOOK


Book Synopsis Applications of Lie Groups to Differential Equations by : Peter J. Olver

Download or read book Applications of Lie Groups to Differential Equations written by Peter J. Olver. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to explaining a wide range of applications of con tinuous symmetry groups to physically important systems of differential equations. Emphasis is placed on significant applications of group-theoretic methods, organized so that the applied reader can readily learn the basic computational techniques required for genuine physical problems. The first chapter collects together (but does not prove) those aspects of Lie group theory which are of importance to differential equations. Applications covered in the body of the book include calculation of symmetry groups of differential equations, integration of ordinary differential equations, including special techniques for Euler-Lagrange equations or Hamiltonian systems, differential invariants and construction of equations with pre scribed symmetry groups, group-invariant solutions of partial differential equations, dimensional analysis, and the connections between conservation laws and symmetry groups. Generalizations of the basic symmetry group concept, and applications to conservation laws, integrability conditions, completely integrable systems and soliton equations, and bi-Hamiltonian systems are covered in detail. The exposition is reasonably self-contained, and supplemented by numerous examples of direct physical importance, chosen from classical mechanics, fluid mechanics, elasticity and other applied areas.

Lie Theory and Its Applications in Physics

2013-04-09 Mathematics
Download Lie Theory and Its Applications in Physics PDF Online Free

Author :
Release : 2013-04-09
Genre : Mathematics
Kind : eBook
Book Rating : 701/5 ( reviews)

GET EBOOK


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. This book was released on 2013-04-09. 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 geometrisation 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. Geometrisation and symmetries are meant in their broadest sense, i.e., classical geometry, differential geometry, groups and quantum groups, infinite-dimensional (super-)algebras, and their representations. Furthermore, we include the necessary tools from functional analysis and number theory. This is a large interdisciplinary and interrelated field. Samples of these new 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 2011. This book is suitable for an extensive audience of mathematicians, mathematical physicists, theoretical physicists, and researchers in the field of Lie Theory.

Structure and Geometry of Lie Groups

2011-11-06 Mathematics
Download Structure and Geometry of Lie Groups PDF Online Free

Author :
Release : 2011-11-06
Genre : Mathematics
Kind : eBook
Book Rating : 944/5 ( reviews)

GET EBOOK


Book Synopsis Structure and Geometry of Lie Groups by : Joachim Hilgert

Download or read book Structure and Geometry of Lie Groups written by Joachim Hilgert. This book was released on 2011-11-06. Available in PDF, EPUB and Kindle. Book excerpt: This self-contained text is an excellent introduction to Lie groups and their actions on manifolds. The authors start with an elementary discussion of matrix groups, followed by chapters devoted to the basic structure and representation theory of finite dimensinal Lie algebras. They then turn to global issues, demonstrating the key issue of the interplay between differential geometry and Lie theory. Special emphasis is placed on homogeneous spaces and invariant geometric structures. The last section of the book is dedicated to the structure theory of Lie groups. Particularly, they focus on maximal compact subgroups, dense subgroups, complex structures, and linearity. This text is accessible to a broad range of mathematicians and graduate students; it will be useful both as a graduate textbook and as a research reference.

You may also like...