The Geometry Of Jordan And Lie Structures PDF Download
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| 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 | : Kevin McCrimmon |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 584 |
| Release | : 2006-05-29 |
| Genre | : Mathematics |
| ISBN | : 0387217967 |
Download A Taste of Jordan Algebras Book in PDF, ePub and Kindle
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 | : 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
| Author | : B. Rosenfeld |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 414 |
| Release | : 2013-03-09 |
| Genre | : Mathematics |
| ISBN | : 147575325X |
Download Geometry of Lie Groups Book in PDF, ePub and Kindle
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 | : Radu Iordănescu |
| Publisher | : |
| Total Pages | : 201 |
| Release | : 2003-12 |
| Genre | : Geometry, Differential |
| ISBN | : 9789732709566 |
Download Jordan Structures in Geometry and Physics Book in PDF, ePub and Kindle
| Author | : Erik M. Alfsen |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 470 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461200199 |
Download Geometry of State Spaces of Operator Algebras Book in PDF, ePub and Kindle
In this book we give a complete geometric description of state spaces of operator algebras, Jordan as well as associative. That is, we give axiomatic characterizations of those convex sets that are state spaces of C*-algebras and von Neumann algebras, together with such characterizations for the normed Jordan algebras called JB-algebras and JBW-algebras. These non associative algebras generalize C*-algebras and von Neumann algebras re spectively, and the characterization of their state spaces is not only of interest in itself, but is also an important intermediate step towards the characterization of the state spaces of the associative algebras. This book gives a complete and updated presentation of the character ization theorems of [10]' [11] and [71]. Our previous book State spaces of operator algebras: basic theory, orientations and C*-products, referenced as [AS] in the sequel, gives an account of the necessary prerequisites on C*-algebras and von Neumann algebras, as well as a discussion of the key notion of orientations of state spaces. For the convenience of the reader, we have summarized these prerequisites in an appendix which contains all relevant definitions and results (listed as (AI), (A2), ... ), with reference back to [AS] for proofs, so that this book is self-contained.
| Author | : Khalid Koufany |
| Publisher | : |
| Total Pages | : 84 |
| Release | : 2005 |
| Genre | : Hardy spaces |
| ISBN | : |
Download Jordan Algebras, Geometry of Hermitian Symmetric Spaces and Non-commutative Hardy Spaces Book in PDF, ePub and Kindle
| Author | : J.E. Humphreys |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 189 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461263980 |
Download Introduction to Lie Algebras and Representation Theory Book 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.
