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Varadarajan V.S. — Lie Groups, Lie Algebras, and Their Representations
Varadarajan V.S. — Lie Groups, Lie Algebras, and Their Representations

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Название: Lie Groups, Lie Algebras, and Their Representations

Автор: Varadarajan V.S.

Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1984

Количество страниц: 452

Добавлена в каталог: 22.05.2008

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
Adjoint representation, of a Lie algebra      50
Adjoint representation, of a Lie algebra in its universal enveloping algebra      172
Adjoint representation, of a Lie group      104
Admissible topological group      62
Ado's Theorem      237
Algebraic group, complex      45
Algebraic group, real      45
Algebraic set      23
Analytic group      41
Analytic manifold, complex      21
Analytic manifold, real      20
Analytic structure, real      20
Analytic subgroup of a Lie group      42
Analytic system of tangent spaces      25
Baker — Campbell — Hausdorff formula      114
Bracket, Lie, in a Lie algebra      47
Bracket, Lie, of vector fields      6
Canonical coordinates, of the first kind      88
Canonical coordinates, of the second kind      89
Cartan matrix      290
Cartan subalgebra (CSA)      262
Cartan — Killing form      208
Casimir element, associated with a representation of a semisimple Lie algebra      218
Casimir element, of the universal enveloping algebra of a semisimple Lie algebra      217
Casimir polynomial      208
Center, of a Lie algebra      50
Central series, ascending and descending, of a nilpotent Lie algebra      193
Chamber, Weyl      282
Chamber, Weyl, associated with root systems      370 379
Chevalley's theorem, on conjugacy of CSA's of a complex Lie algebra      263
Chevalley's theorem, on invariant polynomials on a semisimple Lie algebra      335
Chevalley's theorem, on polynomials invariant with respect to a finite reflection group      383
Chevalley's theorem, on stabilizers in a finite reflection group      377
Classical groups, compact      46
Classical groups, complex      46
Compact form, of a complex semisimple Lie algebra      348
Compact form, of a complex semisimple Lie group      348
Complexification of a Lie algebra      47
Covering group      62
Covering homomorphism      62
Cyclic vector for a representation      154
Derivation, of an algebra      49
Derived algebra, of a Lie algebra      200
Diffeomorphism      15
Differentiable functions      2
Differentiable manifold      2
Differentiable manifold, dimension of      2
Differentiable mapping      14
Differentiable structure      1
Differentiable structure, of a homomorphism of one Lie group into another      70
Differentiable structure, of a mapping      14
Differential expression      4
Differential operator      6
Differential operator, $\pi$-related to another      14
Differential operator, expression of, at a point      6
Differential operator, formal adjoint of      14
Differential operator, left invariant, on a Lie group      53
Dominant linear function      314
Dynkin diagram      293
Engel's theorem      190
Enveloping algebra, of a Lie group      55
Exponential map      85
Exponential map, differential of      108
Exponential of a matrix      89
Exterior algebra      166
Exterior differential form      11
Exterior differentiation      11
Filtered algebra      176
Filting decomposition      152
Free action of a group      81
Free associative algebra      164
Free Lie algebra      174
Frobenius theorem, global      30
Frobenius theorem, local      28
Fundamental group      61
G-space      74
G-space, transitive      74
Galois extension      149
Germ of a function      3
Graded algebra      176
Graded algebra, associated with a filtered algebra      177
Harish — Chandra's theorem, on the center of the universal enveloping algebra of a semisimple Lie algebra      339
Hilbert's fifth problem      42
Homogeneous space      74
Homomorphism, of Lie algebras      47
Ideal, of a Lie algebra      47
Imbedding      16
Imbedding, quasiregular      17
Imbedding, regular      16
Immersion      16
Infinitesimal character      184 339
Integral linear function      314
Involutive analytic system, of tangent spaces      25
Involutive analytic system, of tangent spaces, canonical      26
Involutive analytic system, of tangent spaces, coordinates adapted to      28
Involutive analytic system, of tangent spaces, integrable      25
Involutive analytic system, of tangent spaces, integral manifold of      25
Jacobi identity      6 47
Jordan decomposition, of an element of a semisimple Lie algebra      215
Jordan decomposition, of an endomorphism of a vector space      151
Levi decomposition, of a Lie algebra      224
Levi decomposition, of an analytic group      245
Levi subalgebra, of a Lie algebra      224
Levi subgroup, of an analytic group      245
Lexicographic ordering, of a real vector space      285
Lie algebra      46
Lie algebra, abelian      48
Lie algebra, of a Lie group      51
Lie algebra, quotient of      48
Lie algebra, structure constants of      47
Lie algebra, subalgebra of      47
Lie group      41
Lie group, analytic action of, on a manifold      75
Lie group, quotient of      80
Lie subalgebra defined by a Lie subgroup      57
Lie subgroup      42
Local homomorphism      63
Locally isomorphic groups      63
Maurer — Cartan forms      138
Maximal torus, of a compact semisimple analytic group      353
Measure, corresponding to an n-form      12
monodromy      63
Nil ideal, of a Lie algebra      206
Nil radical, of a Lie algebra      206
Nil radical, of an analytic group      244
Nil representation, of a Lie algebra      189
Nilpotent analytic group      195 243
Nilpotent component, of an element of a semisimple Lie algebra      215
Nilpotent element, of a semisimple Lie algebra      215
Nilpotent Lie algebra      189
Orbit      80
Orientable manifold      12
Orientation, of a manifold      12
Poincare series, of a graded vector space      381
Poincare — Birkhoff — Witt theorem      168
Positive system of roots      280 370 379
Product manifolds      19
Product, of Lie algebras      48
Product, of Lie groups      41
Quotient, of a manifold relative to a map      16
Radical, of a Lie algebra      204
Radical, of an analytic group      244
Rank, of a Lie algebra      260
Real form, of a complex Lie algebra      133
Reductive Lie algebra      232
Reflection group      369
Reflection, in a vector space      369
Regular element, of a Lie algebra      261
Regular point of an algebraic set      23
Replica, of an endomorphism of a vector space      157
Representation with weights      316
Representation, complex analytic, of a complex Lie group      102
Representation, irreducible      51
Representation, of associative algebra      152
Representation, of Lie algebra      49
Representation, of Lie group      102
Representation, quotient representation of      51 153
Representation, semisimple      153
Representation, subrepresentation of      51 153
Representations, of a Lie algebra, direct sum of      50
Representations, of a Lie algebra, equivalence of      51
Representations, of a Lie algebra, outer tensor product of      50
Representations, of a Lie algebra, tensor product of      50
Root      273 370
Root space decomposition, of a semisimple Lie algebra      274
Root subspace      273
Root system      370
Root system, extended integral      378
Root system, integral      377
Schur's lemma      153
Semidirect product, of analytic groups      228
Semidirect product, of Lie algebras      224
Semisimple analytic group      207
Semisimple component, of an element of a semisimple Lie algebra      215
Semisimple element, of a semisimple Lie algebra      215
Semisimple Lie algebra      204
Simple Lie algebra      211
Simple system of roots      280 370 379
Solvable analytic group      204 243
Solvable Lie algebra      201
Spin representation      329
Stability subgroup      74
Submanifold of a differentiable manifold      18
Submanifold of a differentiable manifold, quasi-regular      18
Submanifold of a differentiable manifold, regular      18
Submersion      15
Symmetric algebra      165
Symmetrizer map      180
Symplectic group      46
Tangent space      3
Tangent space, holomorphic      22
Tangent vector      3
Tangent vector, holomorphic      22
Taylor expansions, on a Lie group      94
Tensor algebra      163
Tensor, degree of      163
Tensor, skew-symmetric      165
Tensor, symmetric      165
Torus      43
Transformation group, global      123
Transformation group, infinitesimal      123
Transformation group, local      122
Unipotent representation, of an analytic group      245
Unipotent subgroup of GL(F)      196
Unitarian trick      349
Universal complexification, of a real analytic group      256
Universal covering group      62
Universal enveloping algebra, of a Lie algebra      167
Vector field      5
Weight, highest, of a representation      317
Weight, of a representation      193 316
Weight, subspace      193 316
Weyl's theorem, on finiteness of fundamental groups of compact semi-simple groups      345
Weyl's theorem, on semisimplicity of representations      222 348
Weyl, basis      280
Weyl, character formula of      366
Weyl, dimension formula of      327 368
Weyl, group      279
Weyl, integral formula of      363
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