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. Structure and Representations of Jordan Algebras available in PDF, EPUB and Kindle.
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.
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.
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.
The Minnesota Notes on Jordan Algebras and Their Applications
The Minnesota Notes on Jordan Algebras and Their Applications - 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 Minnesota Notes on Jordan Algebras and Their Applications write by Max Koecher. This book was released on 2006-11-14. The Minnesota Notes on Jordan Algebras and Their Applications available in PDF, EPUB and Kindle. This volume contains a re-edition of Max Koecher's famous Minnesota Notes. The main objects are homogeneous, but not necessarily convex, cones. They are described in terms of Jordan algebras. The central point is a correspondence between semisimple real Jordan algebras and so-called omega-domains. This leads to a construction of half-spaces which give an essential part of all bounded symmetric domains. The theory is presented in a concise manner, with only elementary prerequisites. The editors have added notes on each chapter containing an account of the relevant developments of the theory since these notes were first written.
