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The Minnesota Notes on Jordan Algebras and Their Applications : Lecture Notes in Mathematics - Aloys Krieg

The Minnesota Notes on Jordan Algebras and Their Applications

Lecture Notes in Mathematics

By: Max Koecher, Aloys Krieg (Editor), Sebastian Walcher (Editor)

Paperback Published: October 1999
ISBN: 9783540663607
Number Of Pages: 184

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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 & 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.

Domains of Positivityp. 1
Some notions and notationsp. 1
The notion of a domain of positivityp. 5
The automorphisms of a domain of positivityp. 9
Norms of a domain of positivityp. 12
Examplesp. 14
Differential operatorsp. 17
An invariant line elementp. 21
The map y ∝ y#p. 23
Homogeneous domains of positivityp. 29
Notesp. 32
Editors' Notesp. 32
Omega Domainsp. 35
The notion of an ¿-domainp. 35
Some examplesp. 38
The geodesies of an ¿-domainp. 40
Non-associative algebrasp. 45
¿-domains and Jordan algebrasp. 48
Notesp. 50
Editors' Notesp. 51
Jordan Algebrasp. 53
Jordan algebrasp. 53
The radical of a Jordan algebrap. 58
The unit element of a Jordan algebrap. 61
The decomposition theoremp. 64
The inversep. 66
Constructions of Jordan algebrasp. 68
Notesp. 71
Editors' Notesp. 71
Real and Complex Jordan Algebrasp. 73
The quadratic representationp. 73
Mutationsp. 76
A generalization of the fundamental formulap. 78
The exponentialp. 82
The associated Lie algebrap. 85
Direct sumsp. 89
Notesp. 90
Editors' Notesp. 91
Complex Jordan Algebrasp. 93
Minimal polynomial and eigenvaluesp. 93
Minimal relationsp. 95
The minimal decompositionp. 97
Applications of the minimal decompositionp. 99
The eigenvalues of L(u) and P(u)p. 102
The embedding of real Jordan algebrasp. 105
Notesp. 107
Editors' Notesp. 108
Jordan Algebras and Omega Domainsp. 109
The ¿-domain of a Jordan algebrap. 109
The Jordan algebra of an ¿-domainp. 113
Jordan algebras with equivalent ¿-domainsp. 115
Formally real Jordan algebrasp. 117
Homogeneous domains of positivityp. 119
Elementary functions on formally real Jordan algebrasp. 122
Direct sumsp. 124
Notesp. 125
Editors' notesp. 126
Half-Spacesp. 127
The half-space of a semisimple Jordan algebrap. 127
The isotropy group &Htilde;0p. 131
Application to the set Hp. 135
Biholomorphic automorphisms of half-spacesp. 140
Formally real Jordan algebrasp. 142
The bounded symmetric domain &Ztilde;p. 145
Remarks on classificationp. 147
One typical examplep. 148
Notesp. 153
Editors' Notesp. 153
Appendix: The Bergman kernel functionp. 157
Reproducing kernelsp. 157
Domains in complex number spacep. 159
Notesp. 161
Editors' Notesp. 161
Bibliographyp. 163
Indexp. 171
Biographyp. 175
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9783540663607
ISBN-10: 3540663606
Series: Lecture Notes in Mathematics
Audience: General
Format: Paperback
Language: English
Number Of Pages: 184
Published: October 1999
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.39 x 15.6  x 1.07
Weight (kg): 0.29

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