The Minnesota Notes on Jordan Algebras and Their Applications

Max Koecher (auth.), Aloys Krieg, Sebastian Walcher (eds.)3540663606, 9783540663607

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.

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Table of contents :
Domains of positivity….Pages 1-33
Omega domains….Pages 35-51
Jordan algebras….Pages 53-72
Real and complex Jordan algebras….Pages 73-92
Complex Jordan algebras….Pages 93-108
Jordan algebras and omega domains….Pages 109-126
Half-spaces….Pages 127-155