The Minnesota Notes on Jordan Algebras and Their Applications, Issue 1710This 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. |
Contents
I | 1 |
II | 5 |
III | 9 |
IV | 12 |
V | 14 |
VI | 17 |
VII | 21 |
VIII | 23 |
XXXVII | 95 |
XXXVIII | 97 |
XXXIX | 99 |
XL | 102 |
XLI | 105 |
XLII | 107 |
XLIII | 108 |
XLIV | 109 |
IX | 29 |
X | 32 |
XII | 35 |
XIII | 38 |
XIV | 40 |
XV | 45 |
XVI | 48 |
XVII | 50 |
XVIII | 51 |
XIX | 53 |
XX | 58 |
XXI | 61 |
XXII | 64 |
XXIII | 66 |
XXIV | 68 |
XXV | 71 |
XXVII | 73 |
XXIX | 76 |
XXX | 78 |
XXXI | 82 |
XXXII | 85 |
XXXIII | 89 |
XXXIV | 90 |
XXXV | 91 |
XXXVI | 93 |
XLVI | 113 |
XLVII | 115 |
XLVIII | 117 |
XLIX | 119 |
L | 122 |
LI | 124 |
LII | 125 |
LIII | 126 |
LIV | 127 |
LV | 131 |
LVI | 135 |
LVII | 140 |
LVIII | 142 |
LIX | 145 |
LX | 147 |
LXI | 148 |
LXII | 153 |
LXIV | 157 |
LXV | 159 |
LXVI | 161 |
LXVIII | 163 |
LXIX | 171 |
LXX | 175 |
Other editions - View all
The Minnesota Notes on Jordan Algebras and Their Applications Max Krieg Aloys Koecher,Sebastian Walcher No preview available - 2014 |
Common terms and phrases
apply associative subalgebra Aut(A belongs Bergman kernel biholomorphic automorphisms bijective Chapter commute compact complete orthogonal system connected component consider Corollary define definite bilinear form denote differentiable direct sum domain of positivity Editors eigenpolynomial eigenvalues equation exists follows formally real Jordan function fundamental formula geodesic Given GL(X half-space Hence holomorphic Hom(X homogeneous domain idempotent identity implies inverse isomorphic Km[u Koecher L(u² Lemma linear transformation log w(y matrix minimal decomposition minimal polynomial Montecatini Terme Moreover mutation neighborhood nilpotent non-singular norm numbers obtain positive definite Proof prove quadratic representation real Jordan algebra real-analytic resp respect satisfying self-adjoint semisimple Jordan algebra shows Substituting symmetric bilinear form Theorem Theory topology transformation L(u unit element v₁ vector space VIII w-domain Y₁ yields zero მე მთ მყ