Jordan Structures In Lie Algebras PDF Download
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Author | : Antonio Fernández López |
Publisher | : American Mathematical Soc. |
Total Pages | : 314 |
Release | : 2019-08-19 |
Genre | : Jordan algebras |
ISBN | : 1470450860 |
Download Jordan Structures in Lie Algebras Book in PDF, ePub and Kindle
Explores applications of Jordan theory to the theory of Lie algebras. After presenting the general theory of nonassociative algebras and of Lie algebras, the book then 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.
Author | : Wolfgang Bertram |
Publisher | : Springer |
Total Pages | : 285 |
Release | : 2003-07-01 |
Genre | : Mathematics |
ISBN | : 3540444580 |
Download The Geometry of Jordan and Lie Structures Book in PDF, ePub and Kindle
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 | : Cho-Ho Chu |
Publisher | : Cambridge University Press |
Total Pages | : 273 |
Release | : 2011-11-17 |
Genre | : Mathematics |
ISBN | : 1139505432 |
Download Jordan Structures in Geometry and Analysis Book in PDF, ePub and Kindle
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 | : Nathan Jacobson |
Publisher | : American Mathematical Soc. |
Total Pages | : 464 |
Release | : 1968-12-31 |
Genre | : Mathematics |
ISBN | : 082184640X |
Download Structure and Representations of Jordan Algebras Book in PDF, ePub and Kindle
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 | : Alberto Castellón Serrano |
Publisher | : |
Total Pages | : 232 |
Release | : 1997 |
Genre | : Jordan algebras |
ISBN | : |
Download Proceedings of the International Conference on Jordan Structures Book in PDF, ePub and Kindle
Author | : Sh. Ayupov |
Publisher | : Springer Science & Business Media |
Total Pages | : 239 |
Release | : 2013-03-14 |
Genre | : Mathematics |
ISBN | : 9401586055 |
Download Jordan, Real and Lie Structures in Operator Algebras Book in PDF, ePub and Kindle
The theory of operator algebras acting on a Hilbert space was initiated in thirties by papers of Murray and von Neumann. In these papers they have studied the structure of algebras which later were called von Neu mann algebras or W* -algebras. They are weakly closed complex *-algebras of operators on a Hilbert space. At present the theory of von Neumann algebras is a deeply developed theory with various applications. In the framework of von Neumann algebras theory the study of fac tors (i.e. W* -algebras with trivial centres) is very important, since they are comparatively simple and investigation of general W* -algebras can be reduced to the case of factors. Therefore the theory of factors is one of the main tools in the structure theory of von Neumann algebras. In the middle of sixtieth Topping [To 1] and Stormer [S 2] have ini tiated the study of Jordan (non associative and real) analogues of von Neumann algebras - so called JW-algebras, i.e. real linear spaces of self adjoint opera.tors on a complex Hilbert space, which contain the identity operator 1. closed with respect to the Jordan (i.e. symmetrised) product INTRODUCTION 2 x 0 y = ~(Xy + yx) and closed in the weak operator topology. The structure of these algebras has happened to be close to the struc ture of von Neumann algebras and it was possible to apply ideas and meth ods similar to von Neumann algebras theory in the study of JW-algebras.
Author | : Camille Laurent-Gengoux |
Publisher | : Springer Science & Business Media |
Total Pages | : 470 |
Release | : 2012-08-27 |
Genre | : Mathematics |
ISBN | : 3642310907 |
Download Poisson Structures Book in PDF, ePub and Kindle
Poisson structures appear in a large variety of contexts, ranging from string theory, classical/quantum mechanics and differential geometry to abstract algebra, algebraic geometry and representation theory. In each one of these contexts, it turns out that the Poisson structure is not a theoretical artifact, but a key element which, unsolicited, comes along with the problem that is investigated, and its delicate properties are decisive for the solution to the problem in nearly all cases. Poisson Structures is the first book that offers a comprehensive introduction to the theory, as well as an overview of the different aspects of Poisson structures. The first part covers solid foundations, the central part consists of a detailed exposition of the different known types of Poisson structures and of the (usually mathematical) contexts in which they appear, and the final part is devoted to the two main applications of Poisson structures (integrable systems and deformation quantization). The clear structure of the book makes it adequate for readers who come across Poisson structures in their research or for graduate students or advanced researchers who are interested in an introduction to the many facets and applications of Poisson structures.
Author | : Alexander A. Kirillov |
Publisher | : Cambridge University Press |
Total Pages | : 237 |
Release | : 2008-07-31 |
Genre | : Mathematics |
ISBN | : 0521889693 |
Download An Introduction to Lie Groups and Lie Algebras Book in PDF, ePub and Kindle
This book is an introduction to semisimple Lie algebras. It is concise and informal, with numerous exercises and examples.
Author | : Harald Upmeier |
Publisher | : American Mathematical Soc. |
Total Pages | : 95 |
Release | : 1987 |
Genre | : Mathematics |
ISBN | : 082180717X |
Download Jordan Algebras in Analysis, Operator Theory, and Quantum Mechanics Book in PDF, ePub and Kindle
Jordan algebras have found interesting applications in seemingly unrelated areas of mathematics such as operator theory, the foundations of quantum mechanics, complex analysis in finite and infinite dimensions, and harmonic analysis on homogeneous spaces. This book describes some relevant results and puts them in a general framework.
Author | : Tonny A. Springer |
Publisher | : Springer Science & Business Media |
Total Pages | : 202 |
Release | : 1997-12-11 |
Genre | : Mathematics |
ISBN | : 9783540636328 |
Download Jordan Algebras and Algebraic Groups Book in PDF, ePub and Kindle
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