Jordan Structures in Lie Algebras - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Jordan Structures in Lie Algebras write by Antonio Fernández López. This book was released on 2019-08-19. Jordan Structures in Lie Algebras available 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.
The Geometry of Jordan and Lie Structures
The Geometry of Jordan and Lie Structures - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook The Geometry of Jordan and Lie Structures write by Wolfgang Bertram. This book was released on 2003-07-01. The Geometry of Jordan and Lie Structures available 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.
Introduction to Lie Algebras and Representation Theory
Introduction to Lie Algebras and Representation Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Introduction to Lie Algebras and Representation Theory write by J.E. Humphreys. This book was released on 2012-12-06. Introduction to Lie Algebras and Representation Theory available in PDF, EPUB and Kindle. This book is designed to introduce the reader to the theory of semisimple Lie algebras over an algebraically closed field of characteristic 0, with emphasis on representations. A good knowledge of linear algebra (including eigenvalues, bilinear forms, euclidean spaces, and tensor products of vector spaces) is presupposed, as well as some acquaintance with the methods of abstract algebra. The first four chapters might well be read by a bright undergraduate; however, the remaining three chapters are admittedly a little more demanding. Besides being useful in many parts of mathematics and physics, the theory of semisimple Lie algebras is inherently attractive, combining as it does a certain amount of depth and a satisfying degree of completeness in its basic results. Since Jacobson's book appeared a decade ago, improvements have been made even in the classical parts of the theory. I have tried to incor porate some of them here and to provide easier access to the subject for non-specialists. For the specialist, the following features should be noted: (I) The Jordan-Chevalley decomposition of linear transformations is emphasized, with "toral" subalgebras replacing the more traditional Cartan subalgebras in the semisimple case. (2) The conjugacy theorem for Cartan subalgebras is proved (following D. J. Winter and G. D. Mostow) by elementary Lie algebra methods, avoiding the use of algebraic geometry.
Structure and Representations of Jordan Algebras
Structure and Representations of Jordan Algebras - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Structure and Representations of Jordan Algebras write by Nathan Jacobson. This book was released on 1968-12-31. Structure and Representations of Jordan Algebras available 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.
Jordan Structures in Geometry and Analysis
Jordan Structures in Geometry and Analysis - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Jordan Structures in Geometry and Analysis write by Cho-Ho Chu. This book was released on 2011-11-17. Jordan Structures in Geometry and Analysis available 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.
