Jordan Structures In Lie Algebras

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Jordan Structures In Lie Algebras

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Author : Antonio Fernández López
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-08-19

Jordan Structures In Lie Algebras written by Antonio Fernández López 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 2019-08-19 with Mathematics categories.

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.

Structure And Representations Of Jordan Algebras

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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 Geometry And Analysis

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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.

Introduction To Lie Algebras And Representation Theory

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Author : JAMES HUMPHREYS
language : en
Publisher: Springer Science & Business Media
Release Date : 1994-10-27

Introduction To Lie Algebras And Representation Theory written by JAMES HUMPHREYS 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 1994-10-27 with Mathematics categories.

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.

The Geometry Of Jordan And Lie Structures

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Author : Wolfgang Bertram
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-12-12

The Geometry Of Jordan And Lie Structures written by Wolfgang Bertram 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 2000-12-12 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.

Exceptional Lie Algebras And The Structure Of Hermitian Symmetric Spaces

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Author : Daniel Drucker
language : en
Publisher: American Mathematical Soc.
Release Date : 1978

Exceptional Lie Algebras And The Structure Of Hermitian Symmetric Spaces written by Daniel Drucker 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 1978 with Mathematics categories.

This monograph explicitly determines the "orbit structure" of all irreducible hermitian symmetric (IHS) spaces in a unified way by means of Lie algebra calculations, using J. Tits' models of the Lie algebras [script]e6 and [script]e7 in the two "exceptional" cases. An introduction to the theory of hermitian symmetric spaces is included, along with an elementary exposition of the facts from nonassociative algebra needed to understand and use Tits' constructions of all the complex exceptional simple Lie algebras and their real forms

An Introduction To Lie Groups And Lie Algebras

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Author : Alexander Kirillov, Jr
language : en
Publisher: Cambridge University Press
Release Date : 2017-06-30

An Introduction To Lie Groups And Lie Algebras written by Alexander Kirillov, Jr 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 2017-06-30 with Mathematics categories.

This classic graduate text focuses on the study of semisimple Lie algebras, developing the necessary theory along the way. The material covered ranges from basic definitions of Lie groups to the classification of finite-dimensional representations of semisimple Lie algebras. Lie theory, in its own right, has become regarded as a classical branch of mathematics. Written in an informal style, this is a contemporary introduction to the subject which emphasizes the main concepts of the proofs and outlines the necessary technical details, allowing the material to be conveyed concisely. Based on a lecture course given by the author at the State University of New York at Stony Brook, the book includes numerous exercises and worked examples and is ideal for graduate courses on Lie groups and Lie algebras.

Introduction To Lie Algebras

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Author : K. Erdmann
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-09-28

Introduction To Lie Algebras written by K. Erdmann 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 2006-09-28 with Mathematics categories.

Lie groups and Lie algebras have become essential to many parts of mathematics and theoretical physics, with Lie algebras a central object of interest in their own right. This book provides an elementary introduction to Lie algebras based on a lecture course given to fourth-year undergraduates. The only prerequisite is some linear algebra and an appendix summarizes the main facts that are needed. The treatment is kept as simple as possible with no attempt at full generality. Numerous worked examples and exercises are provided to test understanding, along with more demanding problems, several of which have solutions. Introduction to Lie Algebras covers the core material required for almost all other work in Lie theory and provides a self-study guide suitable for undergraduate students in their final year and graduate students and researchers in mathematics and theoretical physics.

Poisson Structures

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Author : Camille Laurent-Gengoux
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-08-27

Poisson Structures written by Camille Laurent-Gengoux 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 2012-08-27 with Mathematics categories.

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.​

A Taste Of Jordan Algebras

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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.