Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
de Graaf W.A. — Lie Algebras: Theory and Algorithms
de Graaf W.A. — Lie Algebras: Theory and Algorithms

Читать книгу
бесплатно

Скачать книгу с нашего сайта нельзя

Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Lie Algebras: Theory and Algorithms

Автор: de Graaf W.A.

Аннотация:

he aim of the present work is two-fold. Firstly it aims at a giving an account of many existing algorithms for calculating with finite-dimensional Lie algebras. Secondly, the book provides an introduction into the theory of finite-dimensional Lie algebras. These two subject areas are intimately related. First of all, the algorithmic perspective often invites a different approach to the theoretical material than the one taken in various other monographs (e.g., [42], [48], [77], [86]). Indeed, on various occasions the knowledge of certain algorithms allows us to obtain a straightforward proof of theoretical results (we mention the proof of the Poincaré-Birkhoff-Witt theorem and the proof of Iwasawa's theorem as examples). Also proofs that contain algorithmic constructions are explicitly formulated as algorithms (an example is the isomorphism theorem for semisimple Lie algebras that constructs an isomorphism in case it exists). Secondly, the algorithms can be used to arrive at a better understanding of the theory. Performing the algorithms in concrete examples, calculating with the concepts involved, really brings the theory of life.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 393

Добавлена в каталог: 04.12.2009

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
$\alpha$-string containing $\beta$      125 131
Abelian Lie algebra      15
Action of a Lie algebra on a vector space      23
Adjoint map      3
Adjoint representation      24
AdjointMatrix      14
Admissible configuration      143
Ado's Theorem      212
Algebra      1
Algebra, associative      1
Algebra, Lie      2
Alternating element      287
Appliance      221 243 245
ArelsomorphicSSLieAlgebras      182
Associative law      2
Automorphism of a Lie algebra      22
Bilinear form      4
BracketingOfHallWord      239 240
Branching rule      301
BranchingRule      302
Canonical basis      155
Canonical generators      153
CanonicalGenerators      154
Cartan matrix      136
Cartan's criterion for semisimplicity      77
Cartan's criterion for solvability      43
CartanMatrixToRootSystem      137
CartanSubalgebraBigField      58
CartanSubalgebraRestricted      59
Casimir operator      81
Casimir operator, universal      280
Central component      29
centralizer      14 15
Centralldempotents      315
Centre      15
Coefficient of a representation      205
CollectionInUAE      193
Commutative Lie algebra      15
Commutator      2
Completely reducible module      24
composition      190 247
Composition series      24
Composition, useful      249
Composition, useless      249
ConjugateDominantWeight      268
Coxeter diagram      143
DecomposeCharacterTensorProduct      300
Decomposing element      105 315
DecompositionBySuccessiveSubtractions      296
Deglex order      186 193
Degree compatible order      193
Degree of free magma elements      218
Derivation      19
Derivation, inner      20
Derivation, outer      20
Derivations      20
Derived series      17
Derived subalgebra      17
DerivedSeries      17
Descending chain condition      186 193 221 241
Diagram automorphism      164
DimensionPolynomial      292
Direct sum of L-modules      24
Direct sum of Lie algebras      21
Direct sum, root systems      129
DirectSumDecomposition      31 108
Dominant integral linear function      263
DominantWeightsOfHWModule      279
Dorroh extension      305
Dynkin diagram      141
Engel's theorem      35
Equivalence of Cartan matrices      136
Equivalence of L-modules      23
Even orthogonal Lie algebra      6
ExtendRepresentation      209
ExtensionSeriesNilpotentCase      203
ExtensionSeriesSolvableCase      203
Faithful representation      23
Finite presentation      220
Finitely presented Lie algebra      220
Fitting decomposition      54
Fitting-null component      54
Fitting-one component      54
FittingOneComponent      55
foliage      232
Formal character      287
Free algebra      218
Free associative algebra      186
Free Lie algebra      219
Free magma      218
Free monoid      186
Freudenthal's multiplicity formula      280
Fundamental dominant weights      266
Groebner basis in a free algebra      222
Groebner basis in a free associative algebra      188
Groebner basis in a free Lie algebra      246
Groebner basis in a universal enveloping algebra      195
Groebner basis, left      201
GroebnerBasis      198 250
Hall order      229
Hall set      229
Hall word      233
HallSet      229
Height of a root      136
Highest weight      122 263
Highest-weight module      263
Highest-weight vector      122 263
Hypercentre      18
Ideal      1
Idempotent      309
Idempotent, central      313
Idempotent, orthogonal      309
Idempotent, primitive      309
Inner automorphism      23
Inner automorphism group      23
Integral linear function      262
InterReduce      250
Irreducible character      295
Irreducible module      24
Irreducible rootsystem      129
IsHallElement      229
Isomorphism of algebras      1
Isomorphism of root systems      129
IsomorphismOfSSLieAlgebras      157
IsRestricted      27
Iwasawa's theorem      215
Jacobi identity      2
Jordan decomposition      312
Killing form      76
Klymik's formula      298
Kostant's formula      294
Largest nilpotency ideal      205
Las Vegas algorithm      12
Leading monomial      186 193
Left-normal form      201
LeftGroebnerBasis      201
LeftNormalForm      201
Leibniz formula      19
Length of a Weyl group element      274
letters      230
Level of a weight      278
Levi subalgebra      89
Levi's theorem      87
LeviSubalgebra      111 118
LeviSubalgebraByLCSeries      112
Lexicographical order      237
Lie bracket      2
Lie polynomial      233
Lie's theorem      41
Linear associative algebra      305
Linear lie algebra      4
Longest element in a Weyl group      275
Lower central series      17
LowerCentralSeries      17
Lyndon — Shirshov words      238
Module      23
Morphism of algebras      1
Morphism of L-modules      23
Multiplication      1
Multiplication table      8
Multiplicative order      186 193 221 241
Multiplicity of a weight      280
Negative root      134
Nilpotency class      17
Nilpotency ideal      205
Nilpotent, associative algebra      306
Nilpotent, element      45
Nilpotent, Lie algebra      17
Nilradical      36
Non-degenerate bilinear form      4
NonNilpotentElement      46
Normal monomials      222 246
Normal words      186 195
NormalForm      187 194 243
normalizer      15 16
Odd orthogonal Lie algebra      6
p-map      26
p-th power mapping      26
Poincare — Birkhoff — Witt theorem      191
Polynomial map      62
Positive root      134
Primary components      50
Primary decomposition      50
PrimaryDecompositionBigField      104
PrimaryDecompositionSmallField      105
Product space      16
ProductSpace      17
Projection matrix      302
Quasi-Hall set      229
Quotient algebra      3
Quotient module      24
QuotientAlgebra      13
Racah's formula      294 297
Radical      307
Radical of an associative algebra      306
Rank of a Lie algebra      57
Rank of a root system      128
Reduced expression (for a Weyl group element)      267
Reduction      187 195
Reduction order      241
Reflecting hyperplane      127
Reflection      127
Regular element      57
Representation      211 215
Representation of a Lie algebra      23
RepresentationNilpotentCase      210
RepresentationSolvableCase      211
Restricted Lie algebra      25
Reverse lexicographical order      239
RewriteMagmaElement      235
Root      60
Root lattice      160
Root order      132
Root order, lexicographical      134
Root space      60
Root space decomposition      60
Root system      127
Root, long      170
Root, short      170
S-element      195
Self-reduced set      188 222 247
Semidirect sum      21
Semisimple, associative algebra      307
Semisimple, Lie algebra      77
Semisimple, linear transformation      311
Serre's theorem      259
Shirshov's theorem      247
Sign of an element of the Weyl group      287
Simple, Lie algebra      77
Simple, reflection      140
Simple, root      134
Simple, system of roots      135
Simple, type      150
SimpleLieAlgebra      172
Simply-laced root system      160
Solvable Lie algebra      17
Solvable radical      38
SolvableRadical      45
Special linear Lie algebra      4
Split, Cartan subalgebra      59
Split, linear Lie algebra      40
Splitting element      102 314
SplittingElementDeterministic      103
SplittingElementRandom      103
Standard factorization      244
Standard monomial      192
Standard sequence      230
Steinberg's formula      297
Structural invariant      121
Structural invariant, complete      121
Structure constants      7
Subalgebra      1
Submodule      24
Symmetric element      287
Symplectic Lie algebra      5
Toral subalgebra      115
ToralSubalgebra      116
Trace form      76
TYPE      180
Type of a semisimple Lie algebra      175
Upper central series      18
UpperCentralSeries      18
Verma module      265
Weight      122 255 262
Weight lattice      266
Weight space      122 255 262
Weight vector      122 255 262
Weight-coordinate vectors      272
WeightsOfHWModule      278
Weyl group      139
Weyl vector      139
Weyl's character formula      291
Weyl's dimension formula      291
Weyl's theorem      83
WeylOrbit      277
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2017
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте