Minoru Wakimoto — Infinite-Dimensional Lie Algebras :: Электронная библиотека попечительского совета мехмата МГУ

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Minoru Wakimoto — Infinite-Dimensional Lie Algebras

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Название: Infinite-Dimensional Lie Algebras

Автор: Minoru Wakimoto

Аннотация:

This volume begins with an introduction to the structure of finite-dimensional simple Lie algebras, including the representation of ${\widehat {\mathfrak {sl}}}(2, {\mathbb C})$, root systems, the Cartan matrix, and a Dynkin diagram of a finite-dimensional simple Lie algebra. Continuing on, the main subjects of the book are the structure (real and imaginary root systems) of and the character formula for Kac-Moody superalgebras, which is explained in a very general setting. Only elementary linear algebra and group theory are assumed. Also covered is modular property and asymptotic behavior of integrable characters of affine Lie algebras. The exposition is self-contained and includes examples. The book can be used in a graduate-level course on the topic.

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Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 2000

Количество страниц: 304

Добавлена в каталог: 31.10.2010

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Предметный указатель

$L_{0}$ -diagonalizable      255
$\alpha$ -series of roots      37
$\mathbb{C}$ -conjugate linear      191
$\mathbb{Z}_{2}$ -graded associative algebra      55
$\mathbb{Z}_{2}$ -graded vector space      50
$\mathfrak{G}$ -invariant      16
$\mathfrak{g}$ -module      6
$\mathfrak{h}$ -diagonalizable      120
Abelian Lie algebra      4
Adjoint representation      13
Affine Kac — Moody algebra      49 100
Affine Lie algebra      49 100
Affine Lie algebra of split type      174
Affine Lie algebra of twisted type      176
Affinization      170
Algebraic conformal field theory      290
Amplitude      231 234
Associative algebra      4
Asymptotic behavior      220
Asymptotic dimension      234
Automorphism of Lie algebras      3
Automorphism of Lie superalgebras      51
BKM algebra      50 89
BKM Lie algebra      89
BKM matrix      74
BKM superalgebra      50 88
BKM supermatrix      74
BPZ series      276
Branching function      270
Canonical central element      179
Cart an involution      191
Cartan matrix      xv 42
Cartan matrix of finite type      42
Cartan subalgebra      28
Cartan's criterion      17
Casimir element      98
Category $\mathcal{O}$       131
Center      3
Central charge      255
CHARACTER      121
Chevalley generators      47
Chevalley involution      184
Classical Lie algebra      45
Classical lie superalgebra      64
Classical theta function      208
Colabel      178
Commutator      2
Compact real form      191
Completely reducible representation of Lie superalgebra      11
Completely reducible, Lie superalgebra      58
Completion      60
Conformal anomaly      259
Conformal invariance constraint      258
Conformal superalgebra      289
Conformal weight      255
Conjugation      51
Connected      111
Contragredient representation      12
Contravariant bilinear form      188
Corank      49
Coset construction      256
Coset representation      263
Coset Virasoro module      263
Coxeter group      110
Coxeter number of affine Lie algebra      180
CSA      289
Decomposable root      38
Dedekind eta function      202
Denominator      125
Denominator identity      xvii 151
Derivation      14
Derived algebra      259
Diagonalizable      28
Dialect      18
Direct sum of Lie algebras      3
Direct sum of representations      10
Discrete series of Virasoro modules      257
Dominant integral form      137
Dual Coxeter number of affme Lie algebra      180
Dual Coxeter number of simple finite dimensional Lie algebra      168
Dual representation      12
Dynkin diagram      43
Elliptic modular function      243
Endomorphism of Lie algebras      3
Endomorphism of Lie superalgebras      51
Energy operator      259
Equivalent representation      12
Euler function      202
Even element      50
Even lattice      206
Even part      50
Even root      65
Exceptional Lie algebra      45
expectation value      184
Extended Dynkin diagram      174
Full dual space      61
Fundamental coroot      77
Fundamental domain      112
Fundamental root      38 77
Fusion algebra      249
Fusion coefficients      245
Fusion coefficients of Virasoro algebra      282
Gauss formulae      203
GCM      xv 48 74
GCM of affine type      99
GCM of finite type      99
GCM of indefinite type      99
Generalized Cartan matrix      xv 74
Generalized Kac — Moody matrix      xvii
GKM algebra      49
GKM Lie algebra      xvii
GKM matrix      xvii
GKM superalgebra      49
GKO construction      256
Growth      234
Height      81
Heisenberg algebra      4
Heisenberg superalgebra      55
Hermitian inner product      191
Highest root      162
Highest weight      255
Highest weight module with highest weight $\Lambda$       122
Highest weight representation      49 122
Highest weight representation of Virasoro algebra      255
Highest weight vector      122 255
Homogeneous      50
Homogeneous degree      50
Homogeneous element      51
Homomorphism of Lie algebras      3
Homomorphism of Lie superalgebras      51
Ideal      2
Ideal of Lie superalgebra      52
Ideal, non-trivial      2
Ideal, proper      2
Ideal, trivial      2 53
Identity transformation      11
Imaginary root      106
Imaginary root of alien-type      112
Imaginary root of domestic-type      112
Indecomposable, BKM supermatrix      75
Indecomposable, Cartan matrix      44
Inner automorphism      15
Inner derivation      14
Integrable representation      122
Intertwining operator      11
Intertwining operator of representations of Lie superalgebras      58
Invariant subspace      10
Invariant subspace of representation of Lie superalgebra      58
Invariant subspace, proper      10
Invariant subspace, trivial      10

Invariant symmetric bilinear form      16
Involution      60
Irreducible representation of Lie algebra      10
Irreducible representation of Lie superalgebra      58
Isomorphism of Lie algebras      3
Isomorphism of Lie superalgebras      51
Jacobi identity      2
Jacobi theta function      214
Jacobi's triple product identity      202
Kac — Moody algebra      48 89
Kac — Moody Lie algebra      xvi 48
Killing form      17
Killing form of Lie superalgebra      64
KM algebra      48
KM matrix      48 74
Kostant's partition function      190
Label      178
Length      155
Lie algebra      2
Lie algebra, quotient      2
Lie sub-superalgebra      52
Lie subalgebra      2
Lie superalgebra      51
Locally impotent      18
Long root      47
Longest element      161 199
Lowest weight      165
Lowest weight module      165
Lowest weight Verma module with lowest weight $-\Lambda$       186
Macdonald identity      204
Mackey observation      49
Maximal abelian subalgebra      28
Maximal weight      265
McKay observation      244
Minimal expression      155
Minimal series      276
Mock theta function      288
Moebius' function      148
Moebius' inversion formula      149
Monster group      49
Moonshine conjecture      49
Multiplicity      81 120
Negative root      81
Non-degenerate      16
Odd element      50
Odd lattice      206
Odd part      50
Odd root      65
Parity      51
Parity of root      94
PBW theorem      9
Poincare — Birkhoff — Witt theorem      9
Polar part      217
Positive root      80
Positive root lattice      110
Positive Weyl chamber      112
Primitive vector      125
Primitive weight      125
Quasi-Dynkin diagram      75
Quotient representation      10
Radical      16
Rank      29
Real form      79
Real root      106
Reduced expression      155
Reducible representation of Lie algebra      10
Reducible representation of Lie superalgebra      58
Reductive Lie algebra      4
Reflection      100
Regular element      38
Representation      6
Representation space      6
Restricted dual space      61
Root      30 80
Root lattice      110
Root space      30 80
Root space decomposition      30
Root vector      30
S-triple      27
Schroedinger representation      11
Schur's lemma      15
Semisimple Lie algebra      4
Shapovalov determinant      190
Short root      47
Signature      101
Simple BKM Lie superalgebra      82
Simple coroot      77
Simple Lie algebra      3
Simple lie superalgebra      53
Simple reflection      102
Simple root      xv 38 77
Simply-laced Lie algebra      46
Singular vector      24 125
Singular weight      24 125
Skew-invariant      108
Special index      192
Specialization      203
Standard bilinear form      47 166
Strange formula      228
String function      265
Subrepresentation      10
Super Jacobi identity      51
Super S-triple      70
Super skew-symmetric bilinear form      54
Super-bracket      51
Super-commutative      55
Super-commutative associative algebra      55
Super-commutator      51
Super-conformal algebra      289
Super-dimension      58
Super-invariance      54
Super-symmetry      54
Support      111
Switching operator      58
Symmetric algebra      8
Symmetric Lie algebra      46
Symmetrizable BKM Lie superalgebra      88
Symmetrizable BKM supermatrix      76
Symmetrizable BKM-superalgebra      88
Symmetrizable Kac — Moody algebra      49
Symmetrization      8
Tauber type theorem      222
Tensor product representation of Lie superalgebra      58
Theta function      208
Tier number      176
Topological conformal field theory      290
Transposed weight      166
Transposed weight of affine Lie algebra      199
Transposition map      12
Triangular decomposition      81
Trivial representation      11
Unitarizable representation      192
Unitarizable representation of Virasoro algebra      256
Unitary trick      25
Universal enveloping algebra      8
Universal property      124
Vector subspace, $\mathbb{Z}_{2}$ -graded      52
Verlinde's formula      246
Verma module      123
Vertex      43
Vertex algebra      49
Virasoro algebra      254
Virasoro conformal algebra      289
Virasoro operator      262
W-skew-invariant      137
wall      112
Weight      120
Weight space      120
Weyl group      101
Weyl vector      93

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