Octonions, Jordan Algebras and Exceptional Groups

1. Front Matter

   Pages I-VIII

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2. Composition Algebras

   • Tonny A. Springer, Ferdinand D. Veldkamp

   Pages 1-23

3. The Automorphism Group of an Octonion Algebra

   • Tonny A. Springer, Ferdinand D. Veldkamp

   Pages 25-36

4. Triality

   • Tonny A. Springer, Ferdinand D. Veldkamp

   Pages 37-67

5. Twisted Composition Algebras

   • Tonny A. Springer, Ferdinand D. Veldkamp

   Pages 69-115

6. J-algebras and Albert Algebras

   • Tonny A. Springer, Ferdinand D. Veldkamp

   Pages 117-160

7. Proper J-algebras and Twisted Composition Algebras

   • Tonny A. Springer, Ferdinand D. Veldkamp

   Pages 161-171

8. Exceptional Groups

   • Tonny A. Springer, Ferdinand D. Veldkamp

   Pages 173-183

9. Cohomological Invariants

   • Tonny A. Springer, Ferdinand D. Veldkamp

   Pages 185-200

10. Back Matter

    Pages 201-208

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The 1963 Göttingen notes of T. A. Springer are well-known in the field but have been unavailable for some time. This book is a translation of those notes, completely updated and revised. The part of the book dealing with the algebraic structures is on a fairly elementary level, presupposing basic results from algebra. In the group-theoretical part use is made of some results from the theory of linear algebraic groups. The book will be useful to mathematicians interested in octonion algebras and Albert algebras, or in exceptional groups. It is suitable for use in a graduate course in algebra.

• Albert Algebras
• Algebraic structure
• Exceptional Groups
• Octonions
• algebra

From the reviews of the first edition:

"This book is an updated and revised English version of the German notes on octaves, Jordan algebras and exceptional groups which appeared as mimeographed lecture notes of Göttingen University in 1963. It is still an excellent reference on the subject … ." (Huberta Lausch, Zentralblatt MATH, Vol. 1087, 2006)

• Mathematisch Instituut, Utrecht, The Netherlands

  Tonny A. Springer

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