Octonions, Jordan Algebras and Exceptional Groups

Tonny A. Springer, born on February 13, 1926 at the Hague, Holland, studied mathematics at the University of Leiden, obtaining his Ph.D. in 1951. He has been at the University of Utrecht since 1955, from 1959-1991 as a full professor, and since 1991 as an emeritus professor. He has held visiting positions at numerous prestigious institutions all over the globe, including the Institute for Advanced Study (Princeton), the Institut des Hautes Etudes Scientifiques (Bures-sur-Yvette) and the Tata Institute of Fundamental Research (Bombay). Throughout his career T. A. Springer has been involved in research on various aspects of the theory of linear algebraic groups (conjugacy classes, Galois cohomology, Weyl groups).

1. Composition Algebras.- 2. The Automorphism Group of an Octonion Algebra.- 3. Triality.- 4. Twisted Composition Algebras.- 5. J-algebras and Albert Algebras.- 6. Proper J-algebras and Twisted Composition Algebras.- 7. Exceptional Groups.- 8. Cohomological Invariants.

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)