Colloquium Publications 1968; 453 pp; softcover Volume: 39 ISBN10: 082184640X ISBN13: 9780821846407 List Price: US$91 Member Price: US$72.80 Order Code: COLL/39.S
 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. Readership Graduate students and research mathematicians interested in Jordan algebras. Table of Contents  Foundations
 Elements of representation theory
 Peirce decompositions and Jordan matrix algebras
 Jordan algebras with minimum conditions on quadratic ideals
 Structure theory for finitedimensional Jordan algebras
 Generic minimum polynomials, traces and norms
 Representation theory for separable Jordan algebras
 Connections with Lie algebras
 Exceptional Jordan algebras
 Further results and open questions
 Bibliography
 Subject index
