The Geometry Of Jordan And Lie Structures

Author : Wolfgang Bertram
Publisher : Springer
Page : 274 pages
File Size : 48,8 Mb
Release : 2003-07-01
Category : Mathematics
ISBN : 9783540444589

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The Geometry of Jordan and Lie Structures by Wolfgang Bertram Pdf

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.

Author : Nathan Jacobson
Publisher : American Mathematical Soc.
Page : 464 pages
File Size : 40,9 Mb
Release : 1968-12-31
Category : Mathematics
ISBN : 9780821846407

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Structure and Representations of Jordan Algebras by Nathan Jacobson Pdf

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.

Author : Cho-Ho Chu
Publisher : Cambridge University Press
Page : 273 pages
File Size : 44,9 Mb
Release : 2011-11-17
Category : Mathematics
ISBN : 9781139505437

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Jordan Structures in Geometry and Analysis by Cho-Ho Chu Pdf

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.

Author : Antonio Fernández López
Publisher : Unknown
Page : 314 pages
File Size : 40,5 Mb
Release : 2019
Category : Electronic
ISBN : 1470453622

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Jordan Structures in Lie Algebras by Antonio Fernández López Pdf

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.

Author : Wolfgang Bertram
Publisher : American Mathematical Soc.
Page : 218 pages
File Size : 42,5 Mb
Release : 2008
Category : Geometry, Differential
ISBN : 9780821840917

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Differential Geometry, Lie Groups and Symmetric Spaces over General Base Fields and Rings by Wolfgang Bertram Pdf

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.

Author : Kevin McCrimmon
Publisher : Springer Science & Business Media
Page : 563 pages
File Size : 44,5 Mb
Release : 2006-05-29
Category : Mathematics
ISBN : 9780387217963

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A Taste of Jordan Algebras by Kevin McCrimmon Pdf

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.

Author : Khalid Koufany
Publisher : Unknown
Page : 84 pages
File Size : 54,5 Mb
Release : 2005
Category : Hardy spaces
ISBN : UOM:39015068671539

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Jordan Algebras, Geometry of Hermitian Symmetric Spaces and Non-commutative Hardy Spaces by Khalid Koufany Pdf

Author : Karl-Hermann Neeb,Arturo Pianzola
Publisher : Springer Science & Business Media
Page : 492 pages
File Size : 50,8 Mb
Release : 2010-10-17
Category : Mathematics
ISBN : 9780817647414

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Developments and Trends in Infinite-Dimensional Lie Theory by Karl-Hermann Neeb,Arturo Pianzola Pdf

This collection of invited expository articles focuses on recent developments and trends in infinite-dimensional Lie theory, which has become one of the core areas of modern mathematics. The book is divided into three parts: infinite-dimensional Lie (super-)algebras, geometry of infinite-dimensional Lie (transformation) groups, and representation theory of infinite-dimensional Lie groups. Contributors: B. Allison, D. Beltiţă, W. Bertram, J. Faulkner, Ph. Gille, H. Glöckner, K.-H. Neeb, E. Neher, I. Penkov, A. Pianzola, D. Pickrell, T.S. Ratiu, N.R. Scheithauer, C. Schweigert, V. Serganova, K. Styrkas, K. Waldorf, and J.A. Wolf.

Author : Jerrold E. Marsden,Tudor S. Ratiu
Publisher : Springer Science & Business Media
Page : 654 pages
File Size : 53,9 Mb
Release : 2007-07-03
Category : Mathematics
ISBN : 9780817644192

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The Breadth of Symplectic and Poisson Geometry by Jerrold E. Marsden,Tudor S. Ratiu Pdf

* The invited papers in this volume are written in honor of Alan Weinstein, one of the world’s foremost geometers * Contributions cover a broad range of topics in symplectic and differential geometry, Lie theory, mechanics, and related fields * Intended for graduate students and working mathematicians, this text is a distillation of prominent research and an indication of future trends in geometry, mechanics, and mathematical physics

Author : Dmitriĭ Vladimirovich Alekseevskiĭ
Publisher : European Mathematical Society
Page : 556 pages
File Size : 53,8 Mb
Release : 2008
Category : Mathematics
ISBN : 3037190515

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Recent Developments in Pseudo-Riemannian Geometry by Dmitriĭ Vladimirovich Alekseevskiĭ Pdf

This book provides an introduction to and survey of recent developments in pseudo-Riemannian geometry, including applications in mathematical physics, by leading experts in the field. Topics covered are: Classification of pseudo-Riemannian symmetric spaces Holonomy groups of Lorentzian and pseudo-Riemannian manifolds Hypersymplectic manifolds Anti-self-dual conformal structures in neutral signature and integrable systems Neutral Kahler surfaces and geometric optics Geometry and dynamics of the Einstein universe Essential conformal structures and conformal transformations in pseudo-Riemannian geometry The causal hierarchy of spacetimes Geodesics in pseudo-Riemannian manifolds Lorentzian symmetric spaces in supergravity Generalized geometries in supergravity Einstein metrics with Killing leaves The book is addressed to advanced students as well as to researchers in differential geometry, global analysis, general relativity and string theory. It shows essential differences between the geometry on manifolds with positive definite metrics and on those with indefinite metrics, and highlights the interesting new geometric phenomena, which naturally arise in the indefinite metric case. The reader finds a description of the present state of the art in the field as well as open problems, which can stimulate further research.

Author : Shima Hirohiko
Publisher : World Scientific
Page : 260 pages
File Size : 46,6 Mb
Release : 2007-02-28
Category : Geometry, Differential
ISBN : 9789814477024

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The Geometry Of Hessian Structures by Shima Hirohiko Pdf

The geometry of Hessian structures is a fascinating emerging field of research. It is in particular a very close relative of Kählerian 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.

Author : Ercüment H. Ortaçgil
Publisher : Oxford University Press
Page : 240 pages
File Size : 41,8 Mb
Release : 2018-06-28
Category : Mathematics
ISBN : 9780192554840

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An Alternative Approach to Lie Groups and Geometric Structures by Ercüment H. Ortaçgil Pdf

This book presents a new and innovative approach to Lie groups and differential geometry. Rather than compiling and reviewing the existing material on this classical subject, Professor Ortaçgil instead questions the foundations of the subject, and proposes a new direction. Aimed at the curious and courageous mathematician, this book aims to provoke further debate and inspire further development of this original research.

Author : Ichiro Satake
Publisher : Princeton University Press
Page : 340 pages
File Size : 45,6 Mb
Release : 2014-07-14
Category : Mathematics
ISBN : 9781400856800

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Algebraic Structures of Symmetric Domains by Ichiro Satake Pdf

This book is a comprehensive treatment of the general (algebraic) theory of symmetric domains. Originally published in 1981. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Author : B. Rosenfeld,Bill Wiebe
Publisher : Springer Science & Business Media
Page : 414 pages
File Size : 47,8 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475753257

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Geometry of Lie Groups by B. Rosenfeld,Bill Wiebe Pdf

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.

Author : Tonny Albert Springer
Publisher : Unknown
Page : 168 pages
File Size : 48,8 Mb
Release : 195?
Category : Jordan algebras
ISBN : 0387061045

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Ergebnisse der Mathematik und ihrer Grenzgebiete by Tonny Albert Springer Pdf