The Geometry Of Jordan And Lie Structures
DOWNLOAD
AUDIOBOOK
Download The Geometry Of Jordan And Lie Structures PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get The Geometry Of Jordan And Lie Structures book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
The Geometry Of Jordan And Lie Structures
DOWNLOAD
AUDIOBOOK
Author : Wolfgang Bertram
language : en
Publisher: Springer
Release Date : 2003-07-01
The Geometry Of Jordan And Lie Structures written by Wolfgang Bertram and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-01 with Mathematics categories.
The geometry of Jordan and Lie structures tries to answer the following question: what is the integrated, or geometric, version of real Jordan algebras, - triple systems and - pairs? Lie theory shows the way one has to go: Lie groups and symmetric spaces are the geometric version of Lie algebras and Lie triple systems. It turns out that both geometries are closely related via a functor between them, called the Jordan-Lie functor, which is constructed in this book. The reader is not assumed to have any knowledge of Jordan theory; the text can serve as a self-contained introduction to (real finite-dimensional) Jordan theory.
Jordan Structures In Geometry And Analysis
DOWNLOAD
AUDIOBOOK
Author : Cho-Ho Chu
language : en
Publisher: Cambridge University Press
Release Date : 2011-11-17
Jordan Structures In Geometry And Analysis written by Cho-Ho Chu and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-17 with Mathematics categories.
Jordan theory has developed rapidly in the last three decades, but very few books describe its diverse applications. Here, the author discusses some recent advances of Jordan theory in differential geometry, complex and functional analysis, with the aid of numerous examples and concise historical notes. These include: the connection between Jordan and Lie theory via the Tits–Kantor–Koecher construction of Lie algebras; a Jordan algebraic approach to infinite dimensional symmetric manifolds including Riemannian symmetric spaces; the one-to-one correspondence between bounded symmetric domains and JB*-triples; and applications of Jordan methods in complex function theory. The basic structures and some functional analytic properties of JB*-triples are also discussed. The book is a convenient reference for experts in complex geometry or functional analysis, as well as an introduction to these areas for beginning researchers. The recent applications of Jordan theory discussed in the book should also appeal to algebraists.
Structure And Representations Of Jordan Algebras
DOWNLOAD
AUDIOBOOK
Author : Nathan Jacobson
language : en
Publisher: American Mathematical Soc.
Release Date : 1968-12-31
Structure And Representations Of Jordan Algebras written by Nathan Jacobson and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1968-12-31 with Mathematics categories.
The theory of Jordan algebras has played important roles behind the scenes of several areas of mathematics. Jacobson's book has long been the definitive treatment of the subject. It covers foundational material, structure theory, and representation theory for Jordan algebras. Of course, there are immediate connections with Lie algebras, which Jacobson details in Chapter 8. Of particular continuing interest is the discussion of exceptional Jordan algebras, which serve to explain the exceptional Lie algebras and Lie groups. Jordan algebras originally arose in the attempts by Jordan, von Neumann, and Wigner to formulate the foundations of quantum mechanics. They are still useful and important in modern mathematical physics, as well as in Lie theory, geometry, and certain areas of analysis.
Jordan Structures In Lie Algebras
DOWNLOAD
AUDIOBOOK
Author : Antonio Fernández López
language : en
Publisher:
Release Date : 2019
Jordan Structures In Lie Algebras written by Antonio Fernández López and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with categories.
This book explores applications of Jordan theory to the theory of Lie algebras. It begins with the general theory of nonassociative algebras and of Lie algebras and then focuses on properties of Jordan elements of special types. Then it proceeds to the core of the book, in which the author explains how properties of the Jordan algebra attached to a Jordan element of a Lie algebra can be used to reveal properties of the Lie algebra itself. One of the special features of this book is that it carefully explains Zelmanov's seminal results on infinite-dimensional Lie algebras from this point of vie.
A Taste Of Jordan Algebras
DOWNLOAD
AUDIOBOOK
Author : Kevin McCrimmon
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-05-29
A Taste Of Jordan Algebras written by Kevin McCrimmon 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 2006-05-29 with Mathematics categories.
This book describes the history of Jordan algebras and describes in full mathematical detail the recent structure theory for Jordan algebras of arbitrary dimension due to Efim Zel'manov. Jordan algebras crop up in many surprising settings, and find application to a variety of mathematical areas. No knowledge is required beyond standard first-year graduate algebra courses.
Geometry Of Lie Groups
DOWNLOAD
AUDIOBOOK
Author : B. Rosenfeld
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Geometry Of Lie Groups written by B. Rosenfeld 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 2013-03-09 with Mathematics categories.
This book is the result of many years of research in Non-Euclidean Geometries and Geometry of Lie groups, as well as teaching at Moscow State University (1947- 1949), Azerbaijan State University (Baku) (1950-1955), Kolomna Pedagogical Col lege (1955-1970), Moscow Pedagogical University (1971-1990), and Pennsylvania State University (1990-1995). My first books on Non-Euclidean Geometries and Geometry of Lie groups were written in Russian and published in Moscow: Non-Euclidean Geometries (1955) [Ro1] , Multidimensional Spaces (1966) [Ro2] , and Non-Euclidean Spaces (1969) [Ro3]. In [Ro1] I considered non-Euclidean geometries in the broad sense, as geometry of simple Lie groups, since classical non-Euclidean geometries, hyperbolic and elliptic, are geometries of simple Lie groups of classes Bn and D , and geometries of complex n and quaternionic Hermitian elliptic and hyperbolic spaces are geometries of simple Lie groups of classes An and en. [Ro1] contains an exposition of the geometry of classical real non-Euclidean spaces and their interpretations as hyperspheres with identified antipodal points in Euclidean or pseudo-Euclidean spaces, and in projective and conformal spaces. Numerous interpretations of various spaces different from our usual space allow us, like stereoscopic vision, to see many traits of these spaces absent in the usual space.
The Geometry Of Hessian Structures
DOWNLOAD
AUDIOBOOK
Author : Hirohiko Shima
language : en
Publisher: World Scientific
Release Date : 2007
The Geometry Of Hessian Structures written by Hirohiko Shima 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 Mathematics categories.
The geometry of Hessian structures is a fascinating emerging field of research. It is in particular a very close relative of Knhlerian geometry, and connected with many important pure mathematical branches such as affine differential geometry, homogeneous spaces and cohomology. The theory also finds deep relation to information geometry in applied mathematics. This systematic introduction to the subject first develops the fundamentals of Hessian structures on the basis of a certain pair of a flat connection and a Riemannian metric, and then describes these related fields as applications of the theory."
Analysis And Geometry On Complex Homogeneous Domains
DOWNLOAD
AUDIOBOOK
Author : Jacques Faraut
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-12-10
Analysis And Geometry On Complex Homogeneous Domains written by Jacques Faraut 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 1999-12-10 with Mathematics categories.
A number of important topics in complex analysis and geometry are covered in this excellent introductory text. Written by experts in the subject, each chapter unfolds from the basics to the more complex. The exposition is rapid-paced and efficient, without compromising proofs and examples that enable the reader to grasp the essentials. The most basic type of domain examined is the bounded symmetric domain, originally described and classified by Cartan and Harish- Chandra. Two of the five parts of the text deal with these domains: one introduces the subject through the theory of semisimple Lie algebras (Koranyi), and the other through Jordan algebras and triple systems (Roos). Larger classes of domains and spaces are furnished by the pseudo-Hermitian symmetric spaces and related R-spaces. These classes are covered via a study of their geometry and a presentation and classification of their Lie algebraic theory (Kaneyuki). In the fourth part of the book, the heat kernels of the symmetric spaces belonging to the classical Lie groups are determined (Lu). Explicit computations are made for each case, giving precise results and complementing the more abstract and general methods presented. Also explored are recent developments in the field, in particular, the study of complex semigroups which generalize complex tube domains and function spaces on them (Faraut). This volume will be useful as a graduate text for students of Lie group theory with connections to complex analysis, or as a self-study resource for newcomers to the field. Readers will reach the frontiers of the subject in a considerably shorter time than with existing texts.
Jordan Algebras And Algebraic Groups
DOWNLOAD
AUDIOBOOK
Author : Tonny A. Springer
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-12-11
Jordan Algebras And Algebraic Groups written by Tonny A. Springer 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 1997-12-11 with Mathematics categories.
From the reviews: "This book presents an important and novel approach to Jordan algebras. [...] Springer's work will be of service to research workers familiar with linear algebraic groups who find they need to know something about Jordan algebras and will provide Jordan algebraists with new techniques and a new approach to finite-dimensional algebras over fields." American Scientist
Differential Geometry Lie Groups And Symmetric Spaces Over General Base Fields And Rings
DOWNLOAD
AUDIOBOOK
Author : Wolfgang Bertram
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Differential Geometry Lie Groups And Symmetric Spaces Over General Base Fields And Rings written by Wolfgang Bertram and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
The aim of this work is to lay the foundations of differential geometry and Lie theory over the general class of topological base fields and -rings for which a differential calculus has been developed, without any restriction on the dimension or on the characteristic. Two basic features distinguish the author's approach from the classical real (finite or infinite dimensional) theory, namely the interpretation of tangent- and jet functors as functors of scalar extensions and the introduction of multilinear bundles and multilinear connections which generalize the concept of vector bundles and linear connections.
