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Structure and Representations of Jordan Algebras
 
Structure and Representations of Jordan Algebras
eBook ISBN:  978-0-8218-3179-3
Product Code:  COLL/39.E
List Price: $89.00
MAA Member Price: $80.10
AMS Member Price: $71.20
Structure and Representations of Jordan Algebras
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Structure and Representations of Jordan Algebras
eBook ISBN:  978-0-8218-3179-3
Product Code:  COLL/39.E
List Price: $89.00
MAA Member Price: $80.10
AMS Member Price: $71.20
  • Book Details
     
     
    Colloquium Publications
    Volume: 391968; 453 pp
    MSC: Primary 17

    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
     
     
    • Chapters
    • Chapter 1. Foundations
    • Chapter 2. Elements of representation theory
    • Chapter 3. Peirce decompositions and Jordan matrix algebras
    • Chapter 4. Jordan algebras with minimum conditions on quadratic ideals
    • Chapter 5. Structure theory for finite-dimensional Jordan algebras
    • Chapter 6. Generic minimum polynomials, traces and norms
    • Chapter 7. Representation theory for separable Jordan algebras
    • Chapter 8. Connections with Lie algebras
    • Chapter 9. Exceptional Jordan algebras
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 391968; 453 pp
MSC: Primary 17

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.

  • Chapters
  • Chapter 1. Foundations
  • Chapter 2. Elements of representation theory
  • Chapter 3. Peirce decompositions and Jordan matrix algebras
  • Chapter 4. Jordan algebras with minimum conditions on quadratic ideals
  • Chapter 5. Structure theory for finite-dimensional Jordan algebras
  • Chapter 6. Generic minimum polynomials, traces and norms
  • Chapter 7. Representation theory for separable Jordan algebras
  • Chapter 8. Connections with Lie algebras
  • Chapter 9. Exceptional Jordan algebras
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
Please select which format for which you are requesting permissions.