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.
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.
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.
Geometry of Lie Groups
Geometry of Lie Groups - 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 Geometry of Lie Groups write by B. Rosenfeld. This book was released on 1997-02-28. Geometry of Lie Groups available 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.
A Taste of Jordan Algebras
A Taste 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 A Taste of Jordan Algebras write by Kevin McCrimmon. This book was released on 2006-05-29. A Taste of Jordan Algebras available 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.
