Lie Groups and Lie Algebras III: Structure of Lie Groups and Lie AlgebrasA.L. Onishchik, E.B. Vinberg Springer Science & Business Media, 12 juil. 1994 - 250 pages The book contains a comprehensive account of the structure and classification of Lie groups and finite-dimensional Lie algebras (including semisimple, solvable, and of general type). In particular, a modern approach to the description of automorphisms and gradings of semisimple Lie algebras is given. A special chapter is devoted to models of the exceptional Lie algebras. The book contains many tables and will serve as a reference. At the same time many results are accompanied by short proofs. Onishchik and Vinberg are internationally known specialists in their field and well-known for their monograph "Lie Groups and Algebraic Groups" (Springer-Verlag 1990). This Encyclopaedia volume will be immensely useful to graduate students in differential geometry, algebra and theoretical physics. |
Table des matières
I | 7 |
II | 8 |
IV | 10 |
V | 11 |
VI | 12 |
VII | 13 |
VIII | 14 |
IX | 15 |
LXXXVII | 108 |
LXXXVIII | 110 |
LXXXIX | 112 |
XC | 115 |
XCI | 117 |
XCII | 119 |
XCIII | 121 |
XCIV | 123 |
X | 16 |
XII | 17 |
XIII | 18 |
XIV | 19 |
XV | 20 |
XVII | 21 |
XVIII | 22 |
XIX | 24 |
XXI | 25 |
XXII | 27 |
XXIV | 28 |
XXV | 29 |
XXVI | 31 |
XXVII | 32 |
XXVIII | 33 |
XXIX | 35 |
XXX | 36 |
XXXI | 38 |
XXXIII | 39 |
XXXIV | 40 |
XXXV | 41 |
XXXVI | 43 |
XXXVIII | 45 |
XXXIX | 46 |
XL | 48 |
XLII | 49 |
XLIII | 50 |
XLIV | 51 |
XLV | 52 |
XLVII | 53 |
XLVIII | 55 |
XLIX | 56 |
L | 58 |
LI | 59 |
LV | 61 |
LVI | 62 |
LVII | 63 |
LVIII | 65 |
LIX | 66 |
LX | 67 |
LXI | 68 |
LXII | 70 |
LXIII | 72 |
LXIV | 73 |
LXV | 76 |
LXVI | 77 |
LXVII | 79 |
LXVIII | 82 |
LXIX | 83 |
LXX | 85 |
LXXI | 86 |
LXXIII | 88 |
LXXIV | 90 |
LXXV | 91 |
LXXVI | 92 |
LXXVII | 94 |
LXXVIII | 96 |
LXXIX | 99 |
LXXX | 100 |
LXXXI | 102 |
LXXXII | 104 |
LXXXIV | 105 |
LXXXV | 106 |
LXXXVI | 107 |
XCV | 127 |
XCVII | 128 |
XCVIII | 131 |
XCIX | 133 |
C | 134 |
CI | 135 |
CII | 137 |
CIV | 138 |
CV | 139 |
CVII | 141 |
CVIII | 142 |
CIX | 143 |
CXI | 145 |
CXII | 147 |
CXIII | 148 |
CXIV | 149 |
CXV | 151 |
CXVI | 153 |
CXVIII | 154 |
CXIX | 156 |
CXX | 157 |
CXXI | 158 |
CXXII | 160 |
CXXIII | 162 |
CXXIV | 163 |
CXXV | 164 |
CXXVI | 165 |
CXXVII | 167 |
CXXVIII | 169 |
CXXIX | 172 |
CXXX | 173 |
CXXXI | 175 |
CXXXII | 176 |
CXXXIII | 177 |
CXXXIV | 178 |
CXXXV | 182 |
CXXXVII | 184 |
CXXXVIII | 187 |
CXXXIX | 188 |
CXL | 190 |
CXLI | 192 |
CXLII | 193 |
CXLIII | 195 |
CXLIV | 197 |
CXLV | 199 |
CXLVI | 200 |
CXLVII | 203 |
CXLIX | 205 |
CL | 206 |
CLI | 207 |
CLIII | 209 |
CLIV | 212 |
CLV | 213 |
CLVI | 214 |
CLVII | 216 |
CLVIII | 219 |
CLIX | 220 |
CLX | 222 |
CLXI | 224 |
CLXII | 237 |
Autres éditions - Tout afficher
Lie Groups and Lie Algebras III: Structure of Lie Groups and Lie Algebras A. L. Onishchik Affichage d'extraits - 1994 |
Lie Groups and Lie Algebras III: Structure of Lie Groups and Lie Algebras A.L. Onishchik,E.B. Vinberg Aucun aperçu disponible - 2010 |
Expressions et termes fréquents
adjoint representation algebra g algebra of type arbitrary Aut g automorphism bilinear form Cartan decomposition Cartan subalgebra Chap classification coincides commutative complex algebraic group complex Lie algebra complex Lie group complex semisimple Lie complexification conjugacy conjugate connected Lie group Consider Corollary corresponding defined Denote dim g Dynkin diagram Example finite finite-dimensional g₁ GL(V group Aut highest weight homomorphism invariant involutory isomorphic lattice Let G Lie group G Lie subgroup linear group linear Lie group linear representation linearizable Ln(k Malcev matrices nilpotent elements nilpotent Lie algebras nondegenerate nonzero orthogonal parabolic subalgebras Proof Proposition rad g real semisimple Lie reductive regular subalgebras root system Sect semisimple Lie algebra semisimple Lie group simple Lie algebra simple roots simply-connected solvable Lie group subalgebra of g subgroup of G subspace subsystem system of simple tangent algebra tensors three-dimensional simple subalgebra triangular unique vector space Vinberg Weyl chamber Weyl group