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| Scheunert M. — The Theory of Lie Superalgebras: An Introduction |
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| Предметный указатель |
 -gradation induced by a Z - gradation 7 11 169
 -gradation of a vector space 6
(f,d) algebras of Gell — Mann, Michel, Radicati 133 134
Adjoint operation in a Lie superalgebra 244
Adjoint operation, generalized, in a Lie superalgebra 246 247
Ado, theorem by 54
Algebra, enveloping, of a Lie superalgebra 19 33 35 40
Algebra, r - graded 8
Algebra, supersymmetric, of a -graded vector space 23 24 26 60
Antipode 21 32 40 41 56
Automorphism of a Lie superalgebra 13 109 110 126 128 129 131 132 184
Blattner, theorem by 63
Cartan Lie superalgebras 169 207
Cartan subalgebra of a Lie superalgebra, definition 110
Casimir element, generalized, for a Lie superalgebra 49 50
Coassociativity of the coproduct 31 58
Commutator algebra 13 127 133 197 232
Component, homogeneous 6
Coproduct of the enveloping algebra 31 39 57 58
Counit of the enveloping algebra 32 59
Djokovic, Hochschild, theorem by 239
Element, even, of a -graded vector space 6
Element, homogeneous, of a graded vector space 6
Element, invariant with respect to a representation 45 50 240
Element, odd, of a -graded vector space 6
Engel, theorem by 236
Enveloping algebra of a Lie superalgebra 19 33 35 40
Even with respect to a -gradation 6
Extension of the base field, case of a Lie superalgebra 13 23 74 102
Extension of the base field, case of a module over a Lie superalgebra 37 38
Filtration of a Lie superalgebra 86—90
Filtration, associated with a Z-gradation of a Lie superalgebra 89 181
Filtration, canonical, of a produced module 56—58
Filtration, canonical, of the enveloping algebra 25 33 56
Filtration, canonical, of W(V) 181
Filtration, transitive, of a Lie superalgebra 87 89 229
Form, invariant bilinear 47 94 95 112 113 117 120 123 126 136 138
Form, n-linear, associated with a graded L-module 48 112
Form, skew-supersymmetric bilinear 47 129 130 132
Form, superhermitean, on a - graded vector space 245
Form, supersymmetric bilinear 47 112 113 129 133
Guillemin, Sternberg, theorem by 71 182
Hilbert space, -graded 244 245
Homogeneous with respect to a gradation 6
Homomorphism of coalgebras 33 60
Homomorphism of graded algebras 8
Homomorphism of graded modules 10
Homomorphism of graded modules over a Lie superalgebra 36 42 44
Homomorphism of graded vector spaces 7
Homomorphism of Lie superalgebras 13 15 231 233
Hopf superalgebra, the enveloping algebra as a 31—33
Ideal, graded 8 117
Index of a representation of a simple Lie algebra 160 258 261
Invariant with respect to a representation 45—50
Inversion of the Z - gradation 9 126 128 131 133 209
Isomorphism of Lie superalgebras, classification theorems 117 119 140 141 148 149 208 209 222 228 239
Isomorphism of Lie superalgebras, definition 13
Isomorphism of Lie superalgebras, embedding theorems 54 63 71 163 180 181 198
Isomorphism of Lie superalgebras, special cases 18 126 128 133 135 140 142 173 181 188 190 196 198 208 223 228 229 232 235
Isomorphism of Lie superalgebras, transition from gr L to L 89 191 202
Jacobi identity, graded 12
Kac, theorem by 222 228
Killing form of a Lie superalgebra 49 94 112 123 127 128 130 135 136 141 160 237
Lie superalgebra of Cartan type 169 207
Lie superalgebra, associated with an associative superalgebra 13 15 231 232
Lie superalgebra, basic classical simple 241 243
Lie superalgebra, bitransitive Z-graded 73 77 149 209
Lie superalgebra, classical simple 101 107 113 115 118 124 139 140 141 229 230
Lie superalgebra, consistently Z - graded 73 74 88 100 113 124 127 128 131 133 170 186 195
Lie superalgebra, definition 12
Lie superalgebra, exceptional classical simple 134 136 146 148
Lie superalgebra, filtered 87 89 191 202
| Lie superalgebra, general linear 14 124—127
Lie superalgebra, irreducible Z - graded 73 88 95
Lie superalgebra, nil potent 236
Lie superalgebra, orthosymplectic 129 132 239
Lie superalgebra, semi-simple 237 238
Lie superalgebra, simple, definition 91
Lie superalgebra, solvable 236 237
Lie superalgebra, special linear 127 128
Lie superalgebra, strictly semi-simple 119
Lie superalgebra, transitive filtered 63 87 90 181
Lie superalgebra, transitive irreducible consistently Z - graded 77 86 89 100 107 148 149 163 208 222 229
Lie superalgebra, transitive Z - graded 73 88 95 172 180 181 187 188 196 198
Lie superalgebra, Z-graded, associated with a filtered Lie superalgebra 88 89 191 202 229
Lie superalgebra, Z-graded, definition 72
Mapping, canonical, of a Lie superalgebra into its enveloping algebra 19 27
Mapping, homogeneous linear 7
Mapping, invariant bilinear 46 57 58
Mapping, invariant linear 46 53 55 133
Mapping, skew-supersymmetric bilinear 47
Mapping, supersymmetric bilinear 47
Module, - graded 10 170
Module, contragredient 42 56
Module, graded, over a Lie superalgebra 14 34 71 236 237 239 243 245
Module, induced graded 52 54 56 240 242
Module, produced graded 54 71
Module, trivial, over a Lie superalgebra 36 41 58 61 240
Module, typical, over a basic classical simple Lie superalgebra 239 243
Multiplication, inverted 12
Odd with respect to a -gradation 6
Poincare, Birkhoff, Witt, theorem by 26 28 51 60 61
Product, direct, graded, of two graded algebras 8 9
Product, semi-direct, of two Lie superalgebras 233
Representation, adjoint, of a Lie superalgebra 15
Representation, adjoint, of the Lie algebra  in the odd subspace  16 93 95 108 141 160
Representation, elementary, of a simple Lie algebra 253
Representation, graded, of a Lie superalgebra 14 34 71 236 237 239 243 245
Representation, induced graded, of a Lie superalgebra 52 54 56 240 242
Representation, orthogonal, of a semi-simple Lie algebra 252
Representation, produced graded, of a Lie superalgebra 54—71
Representation, self-contragredient, of a semi-simple Lie algebra 251
Representation, symplectic, of a semi-simple Lie algebra 252
Representation, typical, of a basic classical simple Lie superalgebra 239 243
Root (even, odd) of a Lie superalgebra 109 121 122 137 138
Root space decomposition of a Lie superalgebra 109 111 120 123 136 139 164
Schur's lemma 46
Star representation of a Lie superalgebra 245
Subalgebra, graded 8
Subspace, graded 6
Super-cocommutativity of the coproduct 31 32 58
Superadjoint of a linear mapping 244
Superadjoint operation in a Lie superalgebra 244 245
Superalgebra, consistently Z - graded 11
Superalgebra, definition 10
Superalgebra, Z- graded 10 11 23 26
Superderi vation inner, of a Lie superalgebra 15 116 185 186 233
Superderi vation inner, of an associative superalgebra 15 40 232
Superderi vation of a Clifford algebra 231 232
Superderi vation of a Lie superalgebra 15 109 116 232 235
Superderi vation of a superalgebra 14 40 47 59 62
Superderi vation of an exterior algebra 169 207
Superderi vation outer, of a Lie superalgebra 233 235
Superstar representation of a Lie superalgebra 245
Supertrace 48 93 126 127
Supertranspose of a linear mapping 44 126
Tensor product of a graded L-module with a graded L’-module 38 39
Tensor product of two graded L-modules 39
Tensor product, graded, of two graded algebras 9 22 23
Tensor product, graded, of two graded modules 10 38
Tensor product, graded, of two graded vector spaces 7
Transitive 73 87 Lie
Vector space, -graded hermitean 243
Vector space, - graded 6
Z-gradation, consistent with a -gradation 11
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