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The Minnesota notes on Jordan algebras and their applications. Edited and annotated by Aloys Krieg and Sebastian Walcher. (English) Zbl 1072.17513
Lecture Notes in Mathematics 1710. Berlin: Springer (ISBN 3-540-66360-6/pbk). ix, 173 p. EUR 54.00; sFr. 49.50; £ 21.00; $ 30.90 (1999).

This volume contains a re-edition of Max Koecher famous Minnesota Notes (see Zbl 0128.03101). 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.

MSC:
17C36Associated manifolds
32M15Hermitian symmetric spaces, bounded symmetric domains, Jordan algebras (analytic spaces)
17-02Research monographs (nonassociative rings and algebras)
17C55Finite dimensional structures