The Minnesota Notes on Jordan Algebras and Their Applications

1999
ISBN: 978-3-540-66360-7
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1710, 184 Seiten, Format (B × H): 155 mm x 233 mm, Gewicht: 304 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Koecher, Max

Walcher, Sebastian

Krieg, Aloys

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie
• Mathematik | Informatik Mathematik Topologie Algebraische Topologie
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik

Inhaltsverzeichnis

Domains of Positivity.- Omega Domains.- Jordan Algebras.- Real and Complex Jordan Algebras.- Complex Jordan Algebras.- Jordan Algebras and Omega Domains.- Half-Spaces.- Appendix: The Bergman kernel function.